Consider the differential equation

x²y'' - (x² + 2x)y' + (x + 2)y = x³.

Verify that y₁ = x is one solution of the associated homogeneous equation. Then show that the method of reduction of order discussed in Section 4.2 leads to a second solution y₂ of the homogeneous equation as well as a particular solution y_p of the nonhomogeneous equation. Form the general solution of the DE on the interval (0, ∞).