Consider the equation (3x2y+2xy+y3)dx+(x2+y2)dy=0(3x^2y + 2xy + y^3)dx + (x^2 + y^2)dy = 0(3x2y+2xy+y3)dx+(x2+y2)dy=0. Is this equation exact?
Yes, it is exact.
No, it is not exact.
It is exact only for x=0x=0x=0.
The exactness depends on the value of yyy.