Chapter 4.3, Problem 19P

To determine

To verify: The equation $a_0{y}^n+a_1{y}^{n-1}+\cdots +a_{n}y=g\left(t\right)$ reduces to $k_0{u}^n+k_1{u}^{n-1}+\cdots +k_{n}u=b_0{t}^3+\cdots +b_m$ when $g\left(t\right)=e^{\alpha t}\left(b_0{t}^3+\cdots +b_m\right)$ and on substituting $y=e^{\alpha t}u\left(t\right)$ and obtain values of $k_0$ and $k_n$.