Question

Verify that the given expression is a solution of the corresponding differential equation.

y = (sin^-1x)² + c; (1 – x²)\(\cfrac{d^2y}{dx^2}-x\cfrac{dy}{dx}=2\)

Answer 1

y = (sin^-1x)² + c .......(1)

Differentiating w.r.t. x, we get

Differentiating again w.r.t. x, we get

Cancelling 2\(\cfrac{dy}{dx}\) throughout, we get

Hence, y = (sin^-1 x)² + c is a solution of the D.E.