Did I solve this diff eq substition problem properly?

[utnip123]

$xy'=yln(xy)$
$xdy=yln(xy)dx$
$\frac{dy}{y}$=$\frac{ln(xy)dx}{x}$

Substitution:

$v=ln(xy)$
$dv$ = $\frac{dy}{y}$-$\frac{dx}{x}$
$dv$-$\frac{dx}{x}$=$\frac{vdx}{x}$

∫$\frac{dv}{v+1}$=∫$\frac{dx}{x}$

$ln(v+1)=ln x + C$

v+1 = Cx
ln(xy) +1 = Cx

Would that basically be the complete answer?

 

[mfb]

It might be interesting to solve this last equation for y=... and verify the answer with the initial equation.