How do you solve (secx)(dy/dx) = e^(y + sinx)?

[dmitriylm]

Homework Statement

(secx)(dy/dx) = e^(y + sinx)

Homework Equations

None

The Attempt at a Solution

Not sure. I know I can do ln of both sides and isolate the y+sinx but then I get stuck with log^(secx)

 

[dmitriylm]

Ok, I got to (e^-y)dy = (e^sinx)(cosx)dx so I should be ok from there. Just posting in case someone is interested in the future.

 

[HallsofIvy]

Right. Writing the equation as sec(x) dy/dx= e^y e^{sin(x)} show that it is separable. e^{-y}dy= cos(x)e^{sin(x)}dx and both of those are easy to integrate.