homogeneous differential equation->separation of variables

**sinichko** · April 12th 2010, 06:30 AM

Let $M(x,y)dx+N(x,y)dy=0$ - be a homogeneous differential equation.
Prove that by the sustitution of:
$x=rcos\theta y=rsin\theta $
it can be solved by Separation of Variables method.

Thanks a lot.

**dwsmith** · April 12th 2010, 09:19 AM

Originally Posted by sinichko

Let $M(x,y)dx+N(x,y)dy=0$ - be a homogeneous differential equation.
Prove that by the sustitution of:
$x=rcos\theta y=rsin\theta $
it can be solved by Separation of Variables method.

Thanks a lot.

$dx=-rsin\theta d\theta$ and $dy=rcos\theta d\theta$

$ M(rcos,rsin)(-rsin\theta d\theta)+N(rcos,rsin)(rcos\theta d\theta)=0 $

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