Solve the following differential equation: `(x^3+y^3)dy-x^2y dx=0`

Explanation

`(x^3+y^3) dy - x^2y dx = 0`

`=>dy/dx = (x^2y)/(x^3+y^3)`

`=>dy/dx = 1/(x/y+y^2/x^2)`

Let `y/x = v => y = vx =>dy/dx = v+x(dv)/dx`

So, our differential equation becomes,

`v+x(dv)/dx = 1/(1/v+v^2) = v/(1+v^3)`

`=>x(dv)/dx = v/(1+v^3) - v = -v^4/(1+v^3)`

`=> -((1+v^3)/v^4) dv = dx/x`

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