in this problem we consider an equation in differential form M dx+N dy=0

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

give implicit general solutions to the differential equation.

F(x,y)=

1 answer

My = 2-4xy
Nx = 2-4xy

F(x,y) = ∫M dx = ∫ 2y-2xy^2 dx = 2xy - x^2y^2 + h(y)

Now, we have

Fy = 2x - 2x^2y + h'(y)
so, h'(y)=0, and h(y) = c

F(x,y) = 2xy - x^2y^2