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#### ognik

##### Active member

- Feb 3, 2015

- 471

I think this is an Euler ODE, so I try $y=x^p, \therefore y'=p x^{p-1}, \therefore y''= p (p-1) x^{p-2}$

Substituting: $x^p p(p-1) + x^p p - n^2 x^p = 0, \therefore p^2 = n^2, \therefore p= \pm n$

$ \therefore y=C_1 x^n + C_2 x^{-n} $?