Solve this differential equation:

$\displaystyle x dy = (y + x^2 + 9 y^2) dx$

I suspect that the trick is to extract the factor:

$\displaystyle \frac {3 y dx - x dy}{x^2 + 9 y^2}$

so as to equate the LHS to $\displaystyle d \left({\tan^{-1} {\frac {3y} x}}\right)$

because the solution is given as:

$\displaystyle \tan^{-1} \frac {3y} x = 3x + c$

and I can't work out how to split it so there's something sensible on the RHS.

Sorry I've been away for so long, I've been busy on ProofWiki.