Question

I need help in figuring out this problem, not sure exactly how to work this as first order differential equation....
Solve the differential equation:
sinx(e^y +1)dx = e^y (1+cosx)dy

Answer 1

seperate the variables is about the easiest thing id say

Answer 2

\[\frac{sin(x)}{ 1+cos(x)}dx = \frac{e^y}{e^y +1}dy\]
\[\int\left(\frac{sin(x)}{ 1+cos(x)}dx = \frac{e^y}{e^y +1}dy\right)\]

Answer 3

notice the each side is closely resembles: \(\int\cfrac{du}{u}\)

Answer 4

the left side is missing a -1/-1 to complete the effect, but we can just add that in there