How Do You Solve This First Degree ODE Involving Hyperbolic Functions?

[bigevil]

Homework Statement

\frac{dy}{dx} = \frac{cosh x cos y + cosh y sin x}{sinh x sin y - sinh y sin x}

I'm really stuck at this one. I don't even know where to start, but I hope that a substitution (ie u = f(x,y)) might be able to put this in a separable form. Any hints please??

Other roads:

1. Hyperbolic cosine/sine identities?

2. Expressing as powers of e?

 

[Billy Bob]

Is there a typo? It's almost exact. The sin x in the numerator looks out of place.

 

[TaiwanCountry]

This is an exact equation.

dy/dx = Numerator/Denominater

D dx - N dy =0

\partialD/\partialy=\partialN/\partialx

u (nearly)=D dx + N dy