Consider a first order ODE in the form M(x,y) + N(x,y)y= 0. (1) Suppose that (1) is not exact as written, but that multiplying both sides of (1) by an integrating factor gives an exact equation.

(a) Derive a necessary condition for to be a function of y alone. (In the process you should derive an ODE that must satisfy.) (b) Let M = x/y, N = 1 in (1). Show that the resulting ODE satisfies the condition you derived in part (a). (c) Use your results from (a) to find (y) that makes the ODE in (b) exact. (d) Use (c) to solve the ODE.

ASAP PLEASE