Question

Problem:
y = tan(2arctanx)

prove that:

(1+x^2)y'' = 2(2y-x)y'

Answer 1

I manged to get a solution for it, but I wanna know what's wrong on this solution.

Answer 2

y = 2tan(arctanx)/1-tan^2(arctanx)

= 2x/1 - x^2

(1-x^2)y = 2x

-2xy + (1-x^2)y' = 2

-2y -2xy' + (-2x)y' + (1-x^2)y'' = 0

(1-x^2)y'' = 2(y - 2x)y'