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=-(27)/(16),a_1=-\frac74`

Then the particular solution to the ODE is

`y_p=-(27)/(16)-\frac74t`