### Author Topic: TT1 Problem 3 (noon)  (Read 2504 times)

#### Victor Ivrii ##### TT1 Problem 3 (noon)
« 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 $y(0)=0$, $y'(0)=0$.

#### Jialu Lin

• Newbie
• • Posts: 2
• Karma: 5 ##### Re: TT1 Problem 3 (noon)
« Reply #1 on: October 16, 2018, 07:42:57 AM »
Here is my solution.
« Last Edit: October 16, 2018, 08:22:52 AM by Jialu Lin »

#### Shengying Yang

• Jr. Member
•  • Posts: 10
• Karma: 17 ##### Re: TT1 Problem 3 (noon)
« Reply #2 on: October 16, 2018, 08:05:30 AM »
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 ##### Re: TT1 Problem 3 (noon)
« Reply #3 on: October 18, 2018, 04:08:44 AM »
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.