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)

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- May 17th 2010, 11:46 AMCrocSubstitution 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 PM11rdc11
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.