What Method Solves the Differential Equation d^2u/dp^2 = p^2 u?

[kuahji]

Stumbled upon

d^2u/dp^2=p^2 u.

I know the answer, however I can not figure out how to solve this. Any ideas at to which method to try?

 

[LCKurtz]

I haven't actually tried it, but my first guess would be a series solution. You might get some kind of Bessel function.