Question

Are the differential equations separable or not?

1. y'= ye^(x+y)
2. y'= ye^(xy)
3. y'= y(xcos(y))

If they are, could you show how? Any help, even on one, would be extremely appreciated!

Answer 1

1.
rewrite
y'= ye^(x+y)
as
y'=y*e^x*e^y
=> dy/(y*e^y) = e^x dx
=> separable.

2.
If separable, not sure how.

3.
y'= y(xcos(y))
dy/dx=y*x*cos(y)
dy/(y*cos(y) = x dx
=> separable