Hi could someone please explain why
(1-x^2)y'' = 2xy'-2y
Many thanks in advance.
Your question has no sens. Or the wording is incomplete.
One cannot explain why an equation is an equation.
Because you have not converted it to homogeneous like other people would have?
Solving the linear ODE : (1-x^2)y'' - 2xy'+2y = 0 is rather easy.
A first solution is obvious. Then the equation can be reduced to a first order linear ODE.
Separate names with a comma.