# Sturm Liouville and Self Adjoint ODEs

1. Nov 30, 2004

### Ed Quanta

So how do I show that when we have a linear second-order differential equation expressed in self adjoint form that the Wronskian W(y1,y2)= C/p(x)

W=y1y2'-y1'y2, and C is a constant, and p is the coefficient where Ly=d^2/dx^2(pu) - d/dx(p1u) +p2u ?

I know Ly1=0 and Ly2= 0 if that helps at all.

2. Dec 1, 2004

### ReyChiquito

why dont you start by writting down the definition for self-adjointness?

then take $(Ly,u)$ and integrate by parts.

Last edited: Dec 1, 2004