Consider the following linear second order nonhomogeneous differential equation. (x 2 + 1)y′′−2xy′ + 2y = 6(x 2 + 1) 2 (a) Verify that y1 = x is a solution to the corresponding homogeneous equation....

Consider the following linear second order nonhomogeneous differential equation.

(x²
+ 1)y′′−2xy′ + 2y = 6(x²
+ 1)
²

^{(a) Verify that y1 = x is a solution to the corresponding homogeneous equation.
(b) Use the reduction of order formula to determine a second linearly independent solution to homogeneous equation.
(c) Use the method of variation of parameters to determine a particular solution, yp to the nonhomogeneous equation and write down a general solution to the nonhomogeneous equation.}