$\displaystyle (3x+y)dy = (x+3y)dx , y(0) = 1$

As it is a homogeneous differential equation I substituted $\displaystyle y=vx$ and I can't solve it further than the following expression :-

$\displaystyle \frac{x}{dx} = \frac {(1+2v)}{(3+v)dv}$

Please simplify it for me.