لا ایک قرار کے ساتھ میں را کے رہا ہے اور میں تو ایک قرار کے حالات میں تویم ہے۔ اور میں کم اپنے اателиی کو بہت ج lanzتا ہوں اور ہم اور ساتھ ہونوجو تھے گے اور اور یہ کہتا ہے کہ آپ جو جس کی ساتھ آہاہ آپ جو بہت بہت بہت گئی گئی اور بہت بہت ہوا ..  اُن کی بہت ایک ایک ابانی ہوے انہوں کو حامسی ہے۔ ان کو اندرسی ملی ایک ایک شخص پر ملی کے بارے میں گوی ایک کچھ تنمید ہے جو انہوں کو مجھے سامنے کو اپریٹ دنیتے ہیں۔ ایک ایک ایک بارے میں ایک بارے میں جنوش لیا ہے۔ جنوش کے بارے میں مجھے سے بہت اکھتے ہیں۔ اسی کو رہا ہے ، اللہ کہا کہا گا جو ایک بارے میں وَاَنْ نَوْ کَانَ رِجَالٌ مِنَ الْئِنْسِ يَعُوذُونَ بِرِجَالٍ مِنَ الْجِنْ فَزَادُوْ هُمْ راہَقَا ان سورة الجن اللہ سپیکس about it اللہ says part of the things that are mentioned he says and from amongst the issues that are taking place there are people from mankind who are seeking assistance from those of jinn kind and those of jinn kind are leading them further astray that's a quranic verse open surah to the jinn and read it یا معشر الجن قادس تک تھا رو توم مِنَ الْئِنْسِ I love that verse because it wakes us up Oh jinn kind you have made enough fools out of mankind اللہ اکبر one of the translations of that verse Oh jinn kind it's enough what you've done you've already taken a lot of these people and hoodwinked them so they would seek the assistance of a jinn who will immediately communicate with a quran that is with you quran that is with you means when Allah created you He created your soul and put it into a uniform known as your body this uniform you're going to take it out when you die and your soul will continue I hope you understand the way I've worded it your soul is the soul Allah has created it He put it into this uniform known as a body when you die you remove your uniform and the soul is gone with that uniform two other elements there is an angelic angel and angelic force and there is a devil that quran from the jinn kind he communicates immediately with that jinn of the man whom you went to go and see and you know what he says this sister has a pinched nerve at the fourth you know vertebra at the bottom of her back and it's in the left corner if you are just to give her for example this piece of paper and tell her to take five roses and cut their petals into that which is not more than 0.01 grams and take 16 lemons and cut them into quarters and put them around those petals and take the piece of paper and burn it and push it into the center then I will actually flick out that pinched nerve so this man with a big beard masha Allah pink turban that is as long as ever masha Allah you know huge item and he tells you say Subhan Allah you say Subhan Allah Subhan Allah Subhan say Alhamdulillahi say Alhamdulillahi right now let me tell you what's wrong with you you need to take this these petals and these lemons and this piece and do this and do that and you need to do everything together and you will be better so you say شکرا جزاکم اللہ خیر you know masha Allah this man did not take any money nothing happened he took your Iman that's what he did and sometimes he doesn't know because he's diamond is also that Chinese one we spoke about Subhan Allah it's a fact so now what happens you come and you do all that and suddenly you are better well you will be better why because the devil has cured you you stole your cure the devil the Jin knows exactly what happened and the Jin knows exactly where you are standing Subhan Allah so you were cured your back is cured masha Allah now that man is a saint do you know that and you send so many people to him but Allah says hang on do you know you can even earn money through stealing do you know that you become an instant millionaire through robbery but that does not make you a person who did something right no you will say wow I got the money but it does not make you right so you saying wow I'm cured but it does not make it right you will be cured but you suffer the consequence of it what is the consequence they will put a tag they dangle something the first thing they did they will laugh at Allah and have insulted the messenger to say ha ha ha ha ha you told them to put their head their head on the ground we promised you we will deviate them here they are they ready to cut lemons and they ready to put roses and they ready to do things that made no sense for us not for you do you know they just took away your iman they made you worship the devil and you don't even know and you're happy you're still saying Allah who Akbar Allah who Akbar may Allah grant us understanding so now they will tell you do you know who did it a member of your family did it why do they say that every time by default that is the answer sometimes they will pinpoint a person's name they will show you look up into the wall when you look up you see a face wow no I'm not joking I'm honest with you you'll see a face the face hey that's my sister-in-law okay right I know I know what happened Wallahi that was the jinn that's all what is the job of the jinn to break your family ties that's point number one go and read the hadith Allah explains it through the blessed lips of that messenger whose mission was to show you how Allah wants to be worshipped and here we are thinking wow you know what this is true I've seen it with my eyes and then they tell you know do you know what just read a lot of salah read a lot of salah so in your heart you're thinking Subhan Allah this cannot be wrong the man is telling me to read Quran he's telling me to read salah but now I hate my sister I hate my sister-in-law I hate my mother my mother is a witch and my auntie is a witch and everybody else is doing so much witchcraft and I am the person everybody is against me and everybody is bombarding me and nobody has done anything nothing at all there are innocent people whom you are accusing because you have worshipped the devil Allah who akbar and we become so deep in it that we cannot do without it my brothers and sisters that's not how a Muslim should operate pray and keep praying I have seen the power of prayer it will deliver you from whatever you have been suffering from believe me but you need to be constant maintain it turn to Allah how can we want Allah to cure us when we are on the wrong page sometimes forget about the wrong page we in the wrong book altogether Allah who akbar and we want Allah to cure us what type of deviation is this wallahi we should understand if someone claims that X and Y did it let me tell you and I am telling you because I know what I am talking about if that jinn was told you are lying the jinn will change the name if the jinn says Abdullah did this to you you say you are lying he says ok Abdulrahman did it to you say no you are lying ok Fatima did it to you you are lying ok Khadija did it to you that proves that the jinn is a liar Allah says the jinn is making fools of you oh man and we are busy saying no he told the truth because you don't know how that man operated the man who gave you the answer you don't even know how he operated but this is what they are doing may Allah سبحانہ ہوں وطعالہ بلسا کیانا man correct his Muslim women colleagues on their appearance and their on for following proper ruling of Islam for example a man corrects a woman that her lipstick is too much ما شاہ اللہ my sister what was he doing looking at that lipstick ما شاہ اللہ the reality is if politely he reminds a Muslim sister I don't think to say your lipstick is too much is actually respectful to be honest with you if I saw a sister you know full make up and whatever the first thing I would do Insha Allah Insha Allah I hope Allah strengthens me to just look down you know and I'm being as realistic as possible my brothers you know I'm trying to word it respectfully don't think that I'm a person who's not a human being I'm just like you so Insha Allah I try my best to look down and I wouldn't embarrass that sister in that condition not at all it's the wrong time and place It's the wrong time and place what are you doing the woman will start hating religious people what are these guys all about no way you get an opportunity you find the right moment you show them that you care for them as a Muslim sister and she's not just an object and slowly but surely wallahi sometimes without speaking it will start improving itself because they will realize that hey you know what hang on I'm not created by Allah to attract the opposite sex and to be honest I've spoken to non Muslim women sometimes when the opportunity has arisen and a lot of them feel no I feel good when all the men look at me I get angry when a man don't look at me man you know it happened to me once we were in an airport in one of the European countries and I walked past and there was this woman who was literally dressed to kill you know and Subhanallah by the help of Allah and I'm relating it to Allah Subhanahu Wa Ta'ala because we are human being I didn't even look it didn't even tickle me and she actually came up to me a little while later and say why didn't you look and I'm like now you want me to look basically you know and I said no sister I respect you so much that I'd appreciate you know and so on and this has happened to me not a long time ago and it's happened to other scholars in the past and I've mentioned this in some of my lectures as well so I think to correct a sister there is a way you know a respectful way a dignified way but it is a duty to do something about it you know when you see something bad you have to correct it so when you correct it you correct it on different levels but you are never harsh the prophet was told by Allah Subhanahu Wa Ta'ala it is because of the mercy of Allah that you are lenient towards them had you been harsh and hard hearted towards them they would have dispersed wallahi the same rule applies you see a muslim and every one of us myself included we need correction imagine if someone comes to you and just starts telling you things and you know you're an idiot and you're useless and what you said and what you did and how you operate you won't appreciate it because that's the nature of man but if you want to correct someone brother you know so on and if it's a sister you don't need to get into all that detail but at least you need to show concern sometimes when muslims have muslim colleagues who are of the opposite sex they prefer to talk to non muslims than their own muslims you know and this is something that beats me I don't understand what's the logic behind it I'm not saying you shouldn't be communicating with any of your colleagues muslim or non muslim but I'm saying the poor sister is firstly a muslim perhaps she looks up to you I know of muslim sisters who've been motivated at workplace just because their male colleagues never miss a salah and the sister says I had a male colleague who never ever missed his salah and I was so embarrassed because I just used to sit through the lunch and do nothing and then I started I said to myself if he does it let me do it and there was no communication it was just looking so this is why we say Subhanallah there is a way of doing things so it is a duty of anyone either one to correct the other but with respect and with wisdom you know we heard the verse beautifully recited earlier on when you are calling towards the path of Allah call with wisdom don't call with the first thing that comes to your head sit think about it make dua to Allah about it ask Allah's guidance about it then do something you might want to send a beautiful email and you know when you send an email there is a way of doing things because if you just send an email to the same sister who is working with you and say sister like the sister just said you wear too much lipstick at work and that is a haram as it is lipstick is red and the color of جہنم is also red come on come on there is a way of talking so you say sister masha Allah may Allah strengthen you may Allah help you may Allah bless you and your loved ones may Allah Subhanahu Wa Ta'ala grant you goodness and greatness I've got so many weaknesses of my own please highlight them if you see them please do not feel bad that I'm highlighting to you something minor that I believe if it wasn't my duty as a Muslim I wouldn't even have bothered but I felt very very slightly that I should perhaps let you know and as I say before I let you know if there is anything that you see in me that needs attention please let me know and the point that I wanted to raise was perhaps if you would like to consider or reconsider the way you wear your makeup I'm trying to wear it carefully this is just an example based on what the sister is saying or it is much more palatable a person will take it and say جس اکم اللہ خیر I appreciate make dua for me I thank you because of how you said it this goes back to the way you talk may Allah grant us goodness and wisdom but it is our duty to correct one another والله عالم it's a complex I know I recall learning the sunnah of Muhammadﷺ of a handshake it's a nice solid handshake you know you just below your thumb this part here meets the same part of the other person and it actually plugs in and you grip it and you break into a little smile and you say السلام علیکم that's the proper sunnah and then you have people giving you the two fingers have you seen that it's like they don't want to shake your hand at all where they're going to be loved by anyone you know they just do this and next thing it's out shake it shake it properly don't worry the fungus on their hands not going to come to you it's a fact this is something he says greet the people that's what he said he greeted with a smile he was a person who used to smile often at the people such and it is reported that he was absolutely free from hypocrisy so much so that when he was sad you could see it in his face it wasn't hidden he was sad you could see I've just upset him because it was on his face with us we so hurt him yeah السلام علیکم and you know you there you want to bash the person but you haven't managed to say anything let them know you know sister I'm hurt what you said what you did is bad I'd rather sort out the mess than to let it grow because a hypocrite wallahi we let the things grow like hypocrites and the women are not the only ones it's seeped into the men honestly we smile at each other and we hug each other and there's a dagger you know we're gone I can imagine it it happens and these are plastic smiles that cause hatred in the ummah don't let it be I'd rather confront a person who's a brother of mine brother I love you I care for you you are a human being you're a Muslim you are my brother in faith I really have a lot of respect I would just like to clarify this one point it's a point that hurt me perhaps you have a clarification they may not like it but they will appreciate it long term that was the messenger remember the Prophet ﷺ joked even with his family members how many of us especially the older people sit with our family members and tell them decent jokes in Islam when we say decent it must not be x rated number one it must never be about another race or color never haram totally prohibitive it must never ever be about another religion totally prohibitive the Qur'an prohibits you to joke about other religions وَلَا تَسُبْ بُلَّدِنَ يَدَعُونَ مِنْ دُونِ اللَّهِ فَیَا سُبْ بُلَّا عَدَوَا بِغَائِرِ عِلْلِ don't ever mock and jeer and joke about others who are calling besides Allah the gods besides Allah because in return they might start joking about Allah and you were the cause of it may Allah protect us all so it is prohibited look at how beautiful these teachings of social conduct are they make cartoons we will never make cartoons never not even about their gods you cannot attack fire with fire and here in Islam we are being taught that even the Prophetﷺ shared lighter moments with his companions so many times we have narrations where they say the Prophetﷺ was sometimes laughed until his bad teeth the moulders were showing Subhan Allah that is a broad smile a very broad smile some narrations say the canines were showing that's also a very broad smile but when he laughed there was a method of laughing that is also part of our social conduct you don't laugh in such a way that your belly goes up and down and there is an earthquake like feeling in the room computer is according to what it has to be that's it because when you laugh so much let me tell you what happened if everything is a joke even when you joke every few minutes there might be some who do that because I have certain friends who do that people will not take you seriously in anything in life that is the result of it and who caused it you caused it why? you want to convert everything into a joke so that means even when you are serious people will say take him lightly not a pinch of salt a whole bag so the Prophetﷺ its part of his character and conduct he shared life moments but the question is for me and you how many of us do do that with those who are closest to us I know of certain people being a counselor myself when we counsel people for their problems and what they have within the homes and so on there are people who will spend hours on end talking to their friends and joking and laughing they come home they cannot share one single joke with the poor wife who is sitting there with the prepared meal waiting for the last two hours not even one and yet they were enjoying they know it in their hearts and minds and the poor wife is probably even doubting where he was


What's up everybody, Jason here for JaspysCaseBase.com. 2023 Definitive Baseball is finally breaking in here guys with this Pikachu number 18, RNB guys. This is for half the league guys. I know it took a little bit of time but this thing has been marinating and I hope we get some monsters here for this RNBs here guys. So again, free spot, if it's sold out. Yankees, Angels in the RNB, Diamondbacks, Red Sox, Dodgers, Reds, A's, Pirates, Giants, Twins, Guardians, Rockies, Marlins, Brewers, Nationals are all in this guys. You get a piece of these teams via the serial number guys, you guys know how it works of course. First number on the left side of the dash. And remember automatically all redemptions go to spot zero even if it's one on one, it still goes to spot zero. And any non numbered cards are randomized to the group. And again, here's the dice roller, here's the customer name. So again, we're gonna do a free spot giveaway. So let's copy the names there, create a new one here. And again, name that number one, gets that free extra spot and we use the same dice roll for the randomizer. One and three, four times. One, two, three and four. Boom, four times, one and a three, four. Andy, Andy was the first one to buy in. I don't even know how long I posted this up. Maybe three, four days ago. One, two, four times, four times. Look at that, rewarded buddy. Boom. Now, four times in the names. One, two, three and four. Four times. Alan down to Andy. And now we're gonna randomize the numbers, zero. One, two, three, four, five, six, seven, eight, nine. One, two, three and four. Four times, four, four, three, down to four guys. And of course, let's match you up here. Alan you have three, Steve with eight, Darren with five and six, Alan with seven, one and zero. Andy with nine. Ashans with two in the end of your free spots number four. So these are the teams that are part of the R&B guys. Quickly alphabetize it, place it there. And like I said guys, in a separate video is gonna be definitive, good luck everybody.


You're a celebrity is where I am from I don't say hello to the libertarians in libertarians. No offense Quincella. Professor Salerno, can you say no offense Quincella please? No offense Quincella. No offense Quincella.


Meanwhile, an ophthalmologist with the University of Elori-Titian Hospital, Professor Dukwe Ademola-Cupola, has called on government at all levels to provide about its lines and relevant ministries and department to prevent childhood blindness in children, especially by providing tangible and non-tangible eye care technology readily accessible and available. Shemetha Kaur, while delivering the 235th inaugural lecture of the University of Elori, titled Illusion to Vision, a symphony of trial and trial of child high health.  Look ahead sir, it's to make tangible and non-tangible technology for eye care readily accessible in terms of being available and affordable to all people who need it. I also look ahead towards a more personalised medicine provided by genetics and new age therapeutics. The ophthalmologist recommended that at least two tertiary levels well equipped child eye care units should be established in each geopolitical zone of the country in order to provide timely assistance. To Use Updates


Welcome back to our lecture series Math 1220, Calculus II for students at Southern Utah University. As usual of your professor today, Dr. Andrew Missildine. Now you might've been thrown off by the title here if you're reading it, Math 2280, what is this? What we're gonna be doing is starting chapter nine in James Stewart's Calculus textbook, which is based upon the topic of differential equations. A differential equation is an equation that involves a derivative of some kind. That is, we'll have an equation that involves some unknown quantity, I should say unknown function, y equals f of x, and the equation's gonna involve a finite number of its derivatives. So we have an equation that could be involving the first derivative, the second derivative, third derivative, et cetera. We'll come and talk about that a little bit more detail in just a second. Now, the differential equations turn out to be very, very important in not just mathematics, but in broad science as well, as one can use differential equations to approach many, many, many real life applications. And so one cannot undersell how important the study of differential equations, how important that study is. Now, it is not our desire to do an extensive coverage of differential equations. Instead, we plan to do just an extended trailer. Most universities will have at least an introductory course to differential equations at Southern Utah University, that class is math 2280. And of course, other programs might have extensive courses in differential equations, many reaching into a graduate program. Differential equations is pretty important, and the prerequisite at a university is typically gonna be calculus two with maybe some linear algebra, because there's a lot of linear algebra in differential equations. Some universities will require it, some don't. It depends on how they approach it, of course. So let's talk about differential equations. Differential equations, like I said, there are equations that involve functions, which typically we'll call that function Y. The solution to a differential equation will be a function. It'll be a function F, right? So what I want you to do is to try to compare differential equations with algebraic equations you've seen in the past, where in algebraic equations, you have some algebraic combination of the variable X for which the variable X is typically a number, a quantity of some kind. With a differential equation, we're gonna have these combinations of the function Y, we're gonna hear Y as a function. Now in an algebraic equation, you'll have like X squared, X cubed, X to the fourth. You have these powers of X showing up. In a differential equation, the powers of Y are actually gonna be the first derivative, the second derivative, the third derivative, et cetera. And so solving a differential equation means looking for a function Y which satisfies the differential relationship. The order of a differential equation is gonna be the highest derivative present in the differential equation. In this course, we'll be mostly interested in first order differential equations. You might see some in the homework questions, involving second order or higher, but for the most part, we're gonna be focused on solving special types of first order differential equations. Let's give you an example of one. So this right here is a first order differential equation. Y prime is equal to X times Y. So how you wanna interpret this equation is the following. We're looking for a function Y whose derivative is the same thing as just multiplication by the variable X. Because again, Y is a function, it's a function of X. So can we find a function whose derivative is no different than just multiplying by X? You could see how that might actually be sort of a useful information. It's like, okay, derivatives can be complicated times with the chain rule, the product rule, the quotient rule, et cetera. If I knew the derivative was just multiply by X, you could use that for efficiency of some kind. Now, in this video, we're not gonna really talk about how one finds a solution of differential equation. I mostly just wanna convince you of what it means to be a solution, right? So what we're gonna do is we're gonna take as our candidate F of X equals E to the X squared over two, power. And I claim this is a solution. This is a solution to the differential equation. Well, how am I gonna check that? Well, when it comes to an equation, you wanna take your variable assignment and you're gonna wanna plug this into the left side of the equation and the right-hand side of the equation. So if we consider the left-hand side, we wanna take the derivative of our substitution Y here. So what is the derivative of F of X? By the usual rules of derivatives. Because we have an exponential expression, the outer derivative will just fit back out itself, E to the X squared over two. But then we have to multiply it by the inner derivative, X squared over two. That by the power rule is gonna give us a two X over two. You'll notice of course that the two's here cancel and we end up with simply just X times E to the X squared over two. And when you compare this to the right-hand side, the right-hand side is supposed to be X times Y, which if you take X times F of X here, you're gonna end up with X times E to the X squared over two. And Bob's your uncle, you see that the left-hand side and the right-hand side are actually equal to each other. So in fact, this right here is, where did it go? This is a solution to our differential equation. But one thing we're gonna see about differential equations is that solutions are not necessarily unique. Take, as another example, take Y to equal the function G of X, which is given as three times E to the X squared over two. Now, when you look at this one, take the left-hand side here, we're supposed to take the derivative of G. Well, the derivative of G is gonna be three times E to the X squared over two times X. Well, that's just the same thing as three X E to the X squared over two. But if you switch things up a little bit, you get X times three E to the X squared over two. And that's the same thing as X times G of X. So you can see that in this situation, we have a second solution to a differential equation. Now, this might not be any surprise, given that algebraic equations can have multiple solutions, right? Quadratic equations typically have two solutions. Maybe that's no surprise here. Now, in some respect, we do wanna consider these two solutions one and the same thing. What I mean is in the following context, if we take Y to equal C times E to the X squared over two, notice that Y prime is gonna equal C, X E to the X squared over two, which is the same thing as X times C E to the X squared over two. This is just X times Y. And so this right here, Y equals C times E to the X squared over two or C is just any real number. This actually turns out to be a more general solution to this differential equation. And the example F and G that we had before are just specific instances of this example right here. The first one where we take C to equal one and the second one where we take C to be equal to three. We could choose any real number. We're gonna come back and talk about this a little bit more in just a second. So in the meanwhile, I wanna take a look at another example of this. So let's take the differential equation Y prime equals one half Y squared minus Y. This is a first order differential equation. What we're claiming is that the, we wanna find a function whose derivative is equal to just a quadratic expression of the original function, one half Y squared minus one. Now it might, again, at this early stage, it might not exactly be obvious to the viewer why would someone want to solve such a differential equation. But, and we're not even gonna talk about how. So we're skipping the Y, we're skipping the how. All we're doing right now is verifying that this right here represents a family of functions because you take any parameter C that you want right here. You can pick any real number C you want and this would be a solution to this differential equation. Now to do that, we check the left-hand side and the right-hand side. The left-hand side, we wanna check the derivative of the proposed function. So taking its derivative, we get one plus C e to the t over one, or one minus C e to the t. In this situation, our variables in play is C here. That's no big deal. Take the derivative, by the quotient rule, we're gonna get low d high. Take the derivative of the top, we're gonna get C e to the t. And then we subtract high d low. The derivative of the bottom can be a negative C e to the t, like so. Square the bottom, here we go. Just doing our little poem right here. We're gonna leave the denominator factored. There's usually never a benefit of multiplying out the denominator when it comes to a fraction like this. Distributing and combining like terms the numerator though actually will prove to be profitable. Distribute the C e to the t right there. Since we have a negative here and a negative here, that's actually a double negative, like so distribute this C e to the t right here. Actually now that I mentioned it, there's a C e to the t common to both. Let's factor this out. Again, this is a positive there. Factor out the C e to the t. What's left over is one minus C e to the t and one plus C e to the t. All over one minus C e to the t squared. You're gonna see that the C e to the t is in the numerator will cancel. The ones will combine to give us a two. And so the derivative of our functions in these two C e to the t over one minus C e to the t quantity squared. That's what we get for the derivative of this function. Let's compare this to the right-hand side. The right-hand side of the function, sorry, of the equation, that should be one half y squared minus one. So taking the function we had here, let's plug it in one half times. Well, what was the function again? You can see it, we can still see it right here. We're gonna take one plus C e to the t over one minus C e to the t, quantity squared minus one. And so what we wanna do is we wanna show that this is, we wanna check, is this equal to the derivative that we found earlier? That's a parenthesis right there. So we wanna check that. So it's gonna take a little bit of work to do. So let us begin by trying to combine some like terms right there. We'll find a common fraction. Now notice we have a one half in front. We'll just leave that alone for right now. If you're squaring a fraction, that means you square the top and you square the denominator. But again, we're gonna leave the denominator factored. In order to combine the fractions, I need to write one with a common denominator, one minus C e to the t quantity squared. As it's one, that'll be the numerator as well. Now in order to combine some like terms, and actually if you're times a by one half, I can stick that in the denominator. So we're gonna get two times one minus C e to the t squared. Now in the numerator, we need to foil some things out. If you foil the one plus C e to the t squared, you're gonna get one plus two C e to the t plus C squared e to the t, like so. That's the first bit. And then we're gonna subtract from it a one, a minus two C e to the t, and then a plus C squared e to the two t. Sorry, kind of ran out of space there. But there will be some terms that cancel.  There's a C squared e to t, they get each other. And then the other ones that are left over, this is actually a double negative again, you're gonna get some positives. And so as you add those together, we end up with four C e to the t all over two times one minus C e to the t squared. Of course, two goes into four two times. Since you're left with a two C e to the t over one minus C e to the t squared. And so this is what our right-hand side turned out to be if we plug in this function. And if we come back and compare, where do we put it? Oh, it's right here. Two C e to the t over one minus C e to the t squared. So you can see that those two expressions are in fact one of the same thing. So this shows us that every function, every function of this form is a solution to this differential equation right here, where it didn't actually matter what the parameter C was, it's gonna turn out to be the same thing. So this shows us how one checks if a function is a solution to a differential equation and not again, I haven't yet talked about how one finds that we'll get to that in the future. We just wanna clarify that we understand what a differential equation means and how one can verify whether we have a solution or not a solution.