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.