# Substitution for diff. eq.

• May 17th 2010, 11:46 AM
Croc
Substitution for diff. eq.
Hi

Having a bit of trouble with what the substition would be to solve this diff. Any ideas? Thanks.

dy/dx = (xy)/(x^2 - y^2)
• May 17th 2010, 12:08 PM
11rdc11
Quote:

Originally Posted by Croc
Hi

Having a bit of trouble with what the substition would be to solve this diff. Any ideas? Thanks.

dy/dx = (xy)/(x^2 - y^2)

divide the right hand side by x^2

$\frac{dy}{dx} = \displaystyle{\frac{\frac{xy}{x^2}}{\frac{x^2}{x^2 } - \frac{y^2}{x^2}}}$

$\frac{dy}{dx} = \displaystyle{\frac{\frac{y}{x}}{1-\bigg(\frac{y}{x}\bigg)^2}}$

now let

$v = \frac{y}{x}$

and

$vx =y$

so

$v + \bigg(\frac{dv}{dx}\bigg)x = \frac{dy}{dx}$

now sub everything in and solve.