- #1

GGGGc

- Homework Statement
- The original equation is -(1-x^(2))y’’+xy’=ky. How to put it in self-adjoint form?

Also, if let x=cos(theta) how to put that form in d^(2)y/dx^(2)=-ky form?

- Relevant Equations
- -(1-x^(2))y’’+xy’=ky

Here’s my work:

The integrating factor I find is (x^(2)-1)^1/2. The self adjoint form I find is

-d/dx (((1-x^(2))^(3/2))*dy/dx))=k(x^(2)-1)^(1/2).

Am I right?

The integrating factor I find is (x^(2)-1)^1/2. The self adjoint form I find is

-d/dx (((1-x^(2))^(3/2))*dy/dx))=k(x^(2)-1)^(1/2).

Am I right?