# Thread: Cant solve this diff equation :X

1. ## Cant solve this diff equation :X

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

I tried everything I just can't separate the variables :X

2. This is a homogeneous equation because both functions in $dx$ and $dy$ are of degree 2. In this case, make the substitution $y=xv$ and $dy = x dv + v dx$. Then your equation becomes

$x^2-x^2 v^2 dx + 2 x^3 v dv = 0$

$x^2(1-v^2) dx = -2x^3 v dv$

$-\frac{x^2}{2 x^3} dx = \frac{v}{1-v^2} dv$

which is separable. Once you solve for $x$ in terms of $v$, you can go back and solve the equation by substituting $v=\frac{y}{x}$ and solve for $y$.