Solve $(1-x^2)dy/dx + 2xy = x(1-x^2)^{1/2}$

Question

Solve $(1-x^2)dy/dx + 2xy = x(1-x^2)^{1/2}$

I resolved all the terms into exact forms but the coefficients were still non separable.

Answer 1

Hint: Write the equation as $$d\left(\dfrac{y}{1-x^2}\right)=\dfrac{x}{(1-x^2)^\frac32}dx$$