The function y = x2 In x is a solution to the differential equation 4x² y" + y = 0. First, use reduction of order to find a second linearly independent solution to the homogeneous equation. Next,...

Extracted text: The function y = x2 In x is a solution to the differential equation 4x² y" + y = 0. First, use reduction of order to find a second linearly independent solution to the homogeneous equation. Next, choose an appropriate method to find a particular solution to the related non-homogeneous equation 4x² y" + y = x² + 1. You may leave your answer in integral form. Finally, give the general solution to the nonhomogeneous equation.