Consider the equation
x2y′′+ 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 + c1x + c2x-1