Question

Solve differential equation:-
\[ \sin^2(x) \frac{d^2y}{dx^2} = 2 y\]
Does anyone know how to reduce this into solvable form?
The answer is :- \( y \tan (x) = C_1 + C_2 (x - \tan (x)) \)

Answer 1

it suffices to show that cot(x) is one solution is solution of above DE. I found no way of reducing it.