For 10 points, identify this order of the differential equation describing the harmonic oscillator.
Every linear ODE of this type with at most three regular singular points can be transformed into the hypergeometric differential equation, whose solution is the hypergeometric function. A homogeneous differential equation of this type must have its solutions's zeros occur alternately according to Sturm's separation theorem. Bessel functions of this kind are singular at the origin. This order is the minimum for which (*) "homogeneous" means that all of an equation's terms contain the dependent variable, or derivatives of such, which means it can be written as a function of the dependent variable that's equal to zero. The Wronskian is first introduced when considering equations of this order. For 10 points, identify this order of the differential equation describing the harmonic oscillator.
Every linear ODE of this type with at most three regular singular points can be transformed into the hypergeometric differential equation, whose solution is the hypergeometric function.
second order [or two; or obvious equivalents]