# homogeneous differential equation->separation of variables

• April 12th 2010, 06:30 AM
sinichko
homogeneous differential equation->separation of variables
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.
• April 12th 2010, 09:19 AM
dwsmith
Quote:

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
$