I want to solve simple differential equation
2x(1+sqrt(x^2-y)) = y'*sqrt(x^2-y)
10x in advance
Well, there's probably some obviously simple approach. In the meantime:
Make the substitution $\displaystyle w^2 = x^2 - y \Rightarrow 2w \frac{dw}{dx} 2x - \frac{dy}{dx} \Rightarrow \frac{dy}{dx} = 2x - 2w \frac{dw}{dx}$.
Then after a little algebra the DE becomes $\displaystyle -w^2 \frac{dw}{dx} = x$ which is seperable. Solve for w and then substitute back $\displaystyle w^2 = x^2 - y$.