# simple differential equation

• April 17th 2008, 12:46 AM
pafpat
simple differential equation
I want to solve simple differential equation

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

• April 17th 2008, 01:06 AM
mr fantastic
Quote:

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 $w^2 = x^2 - y \Rightarrow 2w \frac{dw}{dx} 2x - \frac{dy}{dx} \Rightarrow \frac{dy}{dx} = 2x - 2w \frac{dw}{dx}$.
Then after a little algebra the DE becomes $-w^2 \frac{dw}{dx} = x$ which is seperable. Solve for w and then substitute back $w^2 = x^2 - y$.