So far what we have done so let us recap what we have done so this is your wave equation so what you have is belongs to the full real line, you only have the initial data that is given and because there is no boundary this has a solution. So this is the D'Alembert's solution we found we had a solution D'Alembert's solution and you have a solution for this problem and we have also seen that this is the unique solution by the energy argument by considering the energy you have the unique solution uniqueness is also proved, okay so you have a unique solution you have shown that D'Alembert's solution is the unique solution for this problem this initial problem for the wave equation on a full domain you have a infinite string infinite string at both ends when you give the displacement and the velocity initially you know that vibration of the string for all time you know as a D'Alembert's solution that is actually that is the solution is because of uniqueness.
இது நாம் கண்டுபிடித்த டி -ஆலம்பெர்ட் சொலுயுஷன். என்னிடம் டி-ஆலம்பெர்ட் சொலுயுஷன் உள்ளது. உங்களிடம் இந்த ப்ராப்ளம்-ன் சொலுயுஷன் உள்ளது. மேலும். எனர்ஜி அணுகுமுறையின்படி இந்த சொலுயுஷன் யுனிக் என்பதை ஏற்கனவே நாம் பார்த்தோம். எனர்ஜி-ஐ கன்சிடெர் பண்ணும்போது இது யுனிக் சொலுயுஷன் ஆகிறது.