Chapter 6.3, Problem 35E

To determine

To prove:

If $a_0=0$ and $a_1\ne 0$ in $a_n{y}^{\left(n\right)}\left(x\right)+a_{n-1}{y}^{\left(n-1\right)}\left(x\right)+\mathrm{...}+a_{0}y\left(x\right)=f\left(x\right)$ and $f\left(x\right)=b_m{x}^m+b_{m-1}{x}^{m-1}+\mathrm{...}+b_{1}x+b_0$, then the particular solution is of the form $y_p\left(x\right)=x\left(B_m{x}^m+B_{m-1}{x}^{m-1}+\mathrm{...}+B_{1}x+B_0\right)$.