Critical Points in a system of differential equations

[rreaves]

i am told to investagate the nature of the critical points of the system:

x'=e^y
y'=(e^y)*cos(x)

i am not sure where to begin because x' is always non-zero.

 

[HallsofIvy]

Yes, exactly. And a "critcal point" for a system is a point where both x' and y' are 0 (or undefined). So what does that tell you about the critical points for this system?