Question

Use undetermined coefficients to find the particular solution to 7t + 5=y''+y'-4y У, (t) - Preview Get help: Video Points possible: 1 This is attempt 1 of 2. Post this question to forum License

Answer 1

Suppose $y_p=a_0+a_1t$ is a solution to the ODE. Then ${y_p}'=a_1$ and ${y_p}''=0$, and substituting these into the ODE gives

$a_1-4(a_0+a_1t)=7t+5\implies\begin{cases}-4a_1=7\\-4a_0+a_1=5\end{cases}\implies a_0=-\dfrac{27}{16},a_1=-\dfrac74$

Then the particular solution to the ODE is

$y_p=-\dfrac{27}{16}-\dfrac74t$