Chapter 6.1, Problem 20E

In Problems $19-22$, a particular solution and a fundamental solution set are given for a nonhomogeneous equation and its corresponding homogeneous equation. (a) Find a general solution to the nonhomogeneous equation. (b) Find the solution that satisfies the specified initial conditions.

$x{y}^{‴}-y^{″}=-2$; $y\left(1\right)=2$, $y^{\prime }\left(1\right)=-1$,

$y^{″}\left(1\right)=-4$; $y_p=x^2$; $\left\{1,x,x^3\right\}$