Toronto Math Forum
MAT2442018F => MAT244Tests => Term Test 1 => Topic started by: Victor Ivrii on October 16, 2018, 05:32:34 AM

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

Here is my solution.

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

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.