Suppose M dx + N dy = 0 where M and N are continuous and have OM ON əx ду and that satisfy the exactness continuous partial derivatives condition on an open rectangle R, show that if (x, y.) is in R and F(x, y) = N(x-,s) ds+M(ty) dt then F, = M and Fy = N. Now, using this method with (x, y) = (0,0) to solve the differential equation (x² + y²)dx + 2xy dy = 0.

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