Equation is 1^st order ODE, non-linear, non-separable

1. Test for Exact ODE:

exact

2.

3. General solution:

> restart;

> with(plots):

> f:={seq(x^2/2+y*x+x-y^3/3+3*y=c/3,c=-12..12)}:

> implicitplot(f,x=-6..6,y=-4..4,numpoints=10000);

> g:=x^2/2+y*x+x-y^3/3+3*y=2/3;

> implicitplot(g,x=-5..5,y=-4..4,numpoints=10000);

Note that point where both coefficients