I'm on my last homework problem, and I'm having some difficulty solving it:
$2x(y+1)\ dx - y\ dy = 0, \quad y(0) = -2$
I've gotten it into the form:
$2x = \frac{yy'}{y+1}$
but I don't know how to integrate the right-side. I'm not even sure what technique I would use.
Plugging the problem into Mathematica gives:
$y(x) = -1 - W(e^{1 - x^{2}})$
where W is the Lambert W function ... which I've never even heard of before, so I'm not sure how I'm expected to solve this using typical methods (I'm a chemical engineer).