You can verify by substitution that yc = c1x + c2x−1 is a complementary function for the n...

You can verify by substitution that yc = c1x + c2x−1 is a complementary function for the nonhomogeneous second-order equation

x2y″ + xy′ − y = 72x5.

But before applying the method of variation of parameters, you must first divide this equation by its leading coefficient x2 to rewrite it in the standard form

Thus f(x) = 72x3 in Eq. Now proceed to solve the equations in and thereby derive the particular solution yp = 3x5.