Chapter 6.1, Problem 24E

Let $L\left[y\right]:=y^{‴}-x{y}^{″}+4y^{\prime }-3xy"$, $y_1\left(x\right)=\cos 2x$, and $y_2\left(x\right):=-1/3$. Verify that $L\left[y_1\right]\left(x\right)=x\cos 2x$ and $L\left[y_2\right]\left(x\right)=x$. Then use the superposition principle (linearity) to find a solution to the differential equation:

a. $L\left[y\right]=7x\cos 2x-3x$.

b. $L\left[y\right]=-6x\cos 2x+11x$.