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MAT244--2018F
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MAT244--Tests
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Term Test 1
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TT1 Problem 3 (noon)
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Topic: TT1 Problem 3 (noon) (Read 6315 times)
Victor Ivrii
Administrator
Elder Member
Posts: 2607
Karma: 0
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 $y(0)=0$, $y'(0)=0$.
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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
»
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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, $C_1=\frac{1}{2}, C_2=0$
$$∴y(t)=\frac{1}{2}e^{-7t}-\frac{1}{2}e^t+4te^{-t}$$
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Victor Ivrii
Administrator
Elder Member
Posts: 2607
Karma: 0
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.
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MAT244--2018F
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MAT244--Tests
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Term Test 1
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TT1 Problem 3 (noon)