How can I solve this higher degree first order differential equation?

Find all solutions of the differential equation:

$$(dy/dx)^2 + e^y +cos(x) + 3 = 0$$

I'm having trouble figuring out where to start. Examples I've seen have polynomial terms instead of exponential and trig terms.

Thank you.

• Is $y$ a real function? At least one of the first 3 terms has to be smaller than or equal $-1$. What does that say about the domain of the equation? – Lutz Lehmann Feb 3 '19 at 0:32

Since $$e^y \ge 0$$ and $$\cos x \ge -1$$ we have
$$(y')^2 + e^y + \cos x + 3 \ge 2$$