Consider the equation
x^{2}y′′+ xy′- y = 4x ln x
(a) Verify that x is a solution to the homogeneous equation.
(b) Use the method of reduction of order to derive the second solution to the homogeneous equation as Cx^{-1}
(c) Use the method of variation of parameters to show that the general solution of the equation can be written as
y = x(ln x)^{2}- x ln x + c_{1}x + c_{2}x^{-1}