Efficiently Solve a Non-Linear ODE with Trigonometric Functions [SOLVED]

[1MileCrash]

Help solving this ODE [SOLVED]

Homework Statement

$\frac{dy}{dx} = \frac{e^{-x}cosy - e^{2y}cosx}{-e^{-x}siny+2e^{2y}sinx}$

Homework Equations

The Attempt at a Solution

First, this is non-linear, not a bernoulli, non-separable, and looks hopeful for an exact. But when I take the partials I get the derivatives as being negatives of one-another.
EDIT
Nevermind, I found out what I was doing wrong. I was being lazy and didn't actually write it in differential form, keeping the negative sign when taking the appropriate partials and ended up with the two results being negatives of each other.

 

[lippyka]

The solution isM = -e^(-x)cosy + e^(2y)cosx N = e^(-x)siny - 2e^(2y)sinx Integrating both sides with respect to x: \int M dx = \int N dy -e^(-x)siny + e^(2y)sin(x) = c where c is the constant of integration.