We have the equation M(x,y) dx + N(x,y) dy = 0 or
M (x,y) + N(x,y)dy/dx = 0
M(x,y) = y and N(x,y) = 3 + 3x - y
remember we can solve this and its called "exact" if M(x,y) = Fx (x,y) and N(x,y) = Fy (x,y), where Fx is the partial derivative of F(x,y) with respect to x (treat y as a constant) and Fy is the partial derivative of F(x,y) with respect to y (treat x as a constant) so if we have Fx (x,Y) + Fy (x,y) dy/dx = 0, then F(x,y) is our solution .
ok so the last thing , assuming there exists such a F(x,y) it must be the case that Fxy = Fyx which is true for all continuous F(x,y). By substituting Fx = M and Fy = N we have
My = Nx .
So here Mx = 0 , and Ny = -1 . hmmm, not exact
ok now we move to plan B and introduce an integrating factor
http://www.cliffsnotes.com/study_guide/Integrating-Factors.topicArticleId-19736,articleId-19711.html