An inexact differential equation

[Kaguro]

Homework Statement

Solve the following differential equation:
(siny*cosy +xcos^2(y))dx + xdy=0

Relevant Equations

$\frac{\partial M}{\partial y} \neq \frac{\partial N}{\partial x}$
So equation is inexact.

Here, M = $siny*cosy +xcos^{2}y$ and N = x
$M_y = (1/2)cos(2y) -xsin(2y)$
and $N_x = 1$

Theorems:
If R = $\frac{1}{N} (M_y - N_x) = f(x), then I.F. = e^{ \int f(x) dx}$
If R = $\frac{1}{M} (N_x - M_y) = g(y), then I.F. = e^{ \int g(x) dx}$

Neither is holding true.
What should I do?

I tried writing N = $x(sin^{2}y + cos^{2}y)$ thinking it may help, but it didn't.

 

[fresh_42]

Try to divide by $\cos^2(y)$ and use $\dfrac{d}{dy}\tan(y)=\dfrac{1}{\cos^2(y)}$ and substitute $u = \tan(y)$.