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
$\displaystyle \frac{dy}{dx} = \displaystyle{\frac{\frac{xy}{x^2}}{\frac{x^2}{x^2 } - \frac{y^2}{x^2}}}$
$\displaystyle \frac{dy}{dx} = \displaystyle{\frac{\frac{y}{x}}{1-\bigg(\frac{y}{x}\bigg)^2}}$
now let
$\displaystyle v = \frac{y}{x}$
and
$\displaystyle vx =y$
so
$\displaystyle v + \bigg(\frac{dv}{dx}\bigg)x = \frac{dy}{dx}$
now sub everything in and solve.