Given two functions, M(x, y) and N(x, y), suppose that (?N/?x ??M/?y)/(M ? N)
is a function of x + y. That is, let f(t) be a function suchthat
f(x + y) = (?N/?x ? ?M/?y)/(M ? N)
Assume that you can solve the differential equation
M dx + N dy = 0
by multiplying by an integrating factor ? that makes it exactand that it can also be
written as a function of x + y, ? = g(x + y) for some functiong(t). Give a method
for finding this integrating factor ?, and use it to find thegeneral solution to the
differential equation
(3 + y + xy)dx + (3 + x + xy)dy = 0.
