TT1 Problem 3 (noon)

[Victor Ivrii]

(a) Find the general solution for equation
\begin{equation*}
y''+8y'+7y=-8e^{t} + 24 e^{-t}.
\end{equation*}
(b)  Find solution, satisfying $y(0)=0$, $y'(0)=0$.

[Jialu Lin]

Here is my solution.

[Shengying Yang]

There is a mistake in your answer. Plugging in $y(0)=0$ , you should get $0=C_1+C_2-\frac{1}{2}$ . Therefore, $C_1=\frac{1}{2}, C_2=0$
$$∴y(t)=\frac{1}{2}e^{-7t}-\frac{1}{2}e^t+4te^{-t}$$

[Victor Ivrii]

Jialu did everything right (almost, there is an error in the calculation of the constants, but the answer is correct).

Shengying, the error is in Jialu's solution, the answer is correct.