This questions is about Exact ODES;

(a) (6 points) Given the following differential equation, M(x, y) + N(x, y) dy = 0, dx (6) assume that M, N, My and Nr are continuous on R := (a, B) x (7, 8) and that My(x, y) = Nr(x, y) for each (x, y) E R. Fix any (Xo, yo) E R and show that v(x, y) is a valid po- tential, where a (2 , y ) := M(s, yo) ds + N(x, t) at. yo (b) (2 points) Show that any separable equation M(x) + N(y)y' = 0 is also exact