Problem with Sturm-Liouville equation

[Transcend]

Hi there :rofl: .
I'm having troubles at a point in one Sturm-Liouville problem :grumpy: .

I am trying to convert a generation eqn to the form of a Sturm-Liouville equation. The equation's form is as follows (where a(x),b(x),c(x),d(x) are arbitrary functions):

a(x)y'' + b(x)y'(x) + [c(x) + (LAMBDA)d(x)]y(x) = o

I begin by formatting in y'' + ... form. How do I proceed from here, please?

Ciao,

Transcend

 

[Logarythmic]

If b(x) = a'(x) your equation is in Sturm-Liouville form...

 

[HallsofIvy]

If not, then you need to multiply by some $\mu(x)$ so that it is:
a(x)$\mu(x)$y'' + b(x)$\mu(x)$y'(x) + [c(x) + ($\lambda(x)$)d(x)]$\mu(x)$y(x) = 0

With a'$\mu(x)$+ a$\mu'(x)$= b(x)$\mu(x)$. That gives you a simple differential equation for $\mu(x)$.