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maks197457 [2]
3 years ago
11

Use undetermined coefficients to find the particular solution to 7t + 5=y''+y'-4y У, (t) - Preview Get help: Video Points possib

le: 1 This is attempt 1 of 2. Post this question to forum License
Mathematics
1 answer:
lions [1.4K]3 years ago
5 0

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

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