# Thread: simple differential equation

1. ## simple differential equation

I want to solve simple differential equation

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

2. Originally Posted by pafpat
I want to solve simple differential equation

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

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 $\displaystyle w^2 = x^2 - y$.