Question

The necessary and sufficient condition that mdx+ndy=0 be exact is

Answer 1

Answer:

(1) (a) Mdx + Ndy = 0 is exact if My = Nx (one mark). (b) If Mdx + Ndy = 0 is exact, u(x, y) = 0 is a solution if u = ∫ M(x, y)dx + k(y) where integral is with respect to x (treating y to be a constant) and k(y) is a function of y. k(y) is determined upto a constant by using the relation Uy = N