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);

 

                 

                 

Note that point  where  both coefficients