Solve,
$\displaystyle y\frac{dy}{dx} = 1+2y$
I know this is easy but I have gone blank its seperable but I had trouble integrating for some reason.
thanks
Notice that
$\displaystyle \frac{y}{1 + 2y} ~dy = dx$
Let $\displaystyle u = 2y + 1 \implies du = 2dy$ so
$\displaystyle \frac{\frac{1}{2}(u - 1) }{u}~\frac{1}{2}du = dx$
$\displaystyle \frac{1}{4}\frac{u - 1}{u}~du = dx$
$\displaystyle \frac{1}{4} \left ( 1 - \frac{1}{u} \right ) du = dx$
-Dan