Rewriting Legendre's Equation for Orthogonality

[popo902]

Homework Statement

i was reading on orthogonality of Legenedre's polynomials
and this equation came up

http://www.hit.ac.il/ac/files/shk_b/Differential.Equations/Orthogonality_of_Legendre_polynomials_files/img39.gif

It's a rewritten form of Legendre's equation, but i can't see how to get there
can someone explain how to get there from the original equation?

Homework Equations

Original

http://mathworld.wolfram.com/images/equations/LegendreDifferentialEquation/NumberedEquation1.gif

The Attempt at a Solution

 

[hunt_mat]

It's quite simple:

$$\frac{d}{dx}((1-x^{2})y')=(1-x^{2})y'' -2xy'$$

From the product rule using 1-x^2 and y'

 

[popo902]

i can't believe i didn't see that
haha thank you once again