Differential Equations problem 2

[Mastur]

Homework Statement

$2(2x^2+y^2)dx-xydy=0$

Homework Equations

$let x = yv$

$dx = ydv+vdy$

The Attempt at a Solution

$(4v^2y^2+2y^2)(ydv+vdy)-vy^2dy=0$

$4v^2y^3dv+4v^3y^2dy+2y^3dv+2vy^2dy-vy^2dy=0$

$4v^2y^3dv+2y^3dv+4v^3y^2dy+vy^2dy=0$

$2y^3(2v^2+1)dv+y^2(4v^3+v)dy=0$
dividing all sides by y²
$2y(2v^2+1)dv+(4v^3+v)dy=0$
combining all ydys and vdvs
$\frac{(2v^2+1)dv}{(4v^3+v)}+\frac{dy}{2y}=0$

$\int{\frac{(2v^2dv)}{4v^3+v}}+\int{\frac{dv}{4v^3+v}}+\int{\frac{dy}{2y}}=0$

Err.. I don't know what to do next.. I can only integrate the 3rd integral..

 

[Dick]

Two words. Partial fractions.

 

[Mastur]

Naa, my memory.. I always forgot those!

Thank you very much for reminding!

I'll try to review first that partial fraction. It seems like I have forgotten the process of it already.