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

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. (22). Now proceed to solve the equations in (31) and thereby derive the particular solution
y_p = 3x⁵.

Transcribed Image Text:

x²y" + xy'-y = 72x5.