Hello:

Problem:

Solve the following equation :

$\displaystyle 2y(x+y+2)dx+(y^2-x^2-4x-1)dy=0$

Solution:

I did not get it ..

not separable, not homogeneous, not exact, not linear, not bernoulli

So I tried to use the method of determinating the integrating factor ..

But this failed with me:

$\displaystyle \dfrac{1}{N} \left( \dfrac{\partial M}{\partial y} - \dfrac{ \partial N }{ \partial x} \right) $ is not a function in x only ..

and

$\displaystyle \dfrac{1}{M} \left( \dfrac{\partial M}{\partial y} - \dfrac{ \partial N }{ \partial x} \right) $ is not a function in y only ..

any ideas??