Originally Posted by

**snoopy** I try to solve this differential equation as:

$\displaystyle

P(x,y)=2 x y^{2} \;\;\;; \; Q(x,y)= x^{2 y} -y

$

You have to find $\displaystyle \mu=\mu(z)$ for z = z(x,y) and solve this DE:

$\displaystyle

\frac{\mu'(z)}{\mu(z)} = \frac{\frac{\partial{P}}{\partial{y}}-\frac{\partial{Q}}{\partial{x}}}{\frac{\partial{z} }{\partial{x}}\; Q - \frac{\partial{z}}{\partial{y}}\; P}

$

This DE can be solved only by numerical approach; it is very difficult solve because when you differentiate Q you get something ugly to calculate. Note:

if $\displaystyle \frac{\partial{P}}{\partial{y}} = \frac{\partial{Q}}{\partial{x}}$ would be **exact** and it would be very simple to solve. How to manipulate this equation they would be exact- insert:

$\displaystyle

\frac{\partial{(\mu P)}}{\partial{y}}=\frac{\partial{(\mu Q)}}{x}

$