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## Homework Statement

[itex]2(2x^2+y^2)dx-xydy=0[/itex]

## Homework Equations

[itex]let x = yv[/itex]

[itex]dx = ydv+vdy[/itex]

## The Attempt at a Solution

[itex](4v^2y^2+2y^2)(ydv+vdy)-vy^2dy=0[/itex]

[itex]4v^2y^3dv+4v^3y^2dy+2y^3dv+2vy^2dy-vy^2dy=0[/itex]

[itex]4v^2y^3dv+2y^3dv+4v^3y^2dy+vy^2dy=0[/itex]

[itex]2y^3(2v^2+1)dv+y^2(4v^3+v)dy=0[/itex]

dividing all sides by y

^{2}

[itex]2y(2v^2+1)dv+(4v^3+v)dy=0[/itex]

combining all ydys and vdvs

[itex]\frac{(2v^2+1)dv}{(4v^3+v)}+\frac{dy}{2y}=0[/itex]

[itex]\int{\frac{(2v^2dv)}{4v^3+v}}+\int{\frac{dv}{4v^3+v}}+\int{\frac{dy}{2y}}=0[/itex]

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