(x^3+xy^2+y)dy+(x^2y+y^3+x)dx=0

Question

It is non-exact DE and I'm stuck at making it an exact DE. Need help. Thank you.

Answer 1

so, what have you tried so far?
You need f(x,y) such that
Try writing it as
[y(x^2+y^2) + x] dx + [x(x^2+y^2) + y]dy = 0
With the exception of a factor of 2, that looks a lot like du = 0 where
u = e^(xy) * (x^2+y^2)