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MAT244--2018F
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Q3 TUT 0301
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Topic: Q3 TUT 0301 (Read 5984 times)
Victor Ivrii
Administrator
Elder Member
Posts: 2607
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Q3 TUT 0301
«
on:
October 12, 2018, 06:04:24 PM »
Find a differential equation whose general solution is
$$y=c_1e^{-t/2}+c_2e^{-2t}.$$
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Yunqi(Yuki) Huang
Jr. Member
Posts: 11
Karma: 5
Re: Q3 TUT 0301
«
Reply #1 on:
October 12, 2018, 06:16:38 PM »
in the attchement
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Keyue Xie
Newbie
Posts: 2
Karma: 1
Re: Q3 TUT 0301
«
Reply #2 on:
October 12, 2018, 06:34:41 PM »
$$
y=c_1e^{\frac{-1}2t} + c_2e^{(-2t)}
$$
$$
r_1=\frac{-1}2, r_2=-2
$$
$$
(r+\frac{1}{2})(r+2) = 0
$$
$$
r^2+ 2r+\frac{1}2r +1 = 0
$$
Therefore
$$
r^2+\frac{5}{2}r+1 = 0
$$
$$
2r^2 + 5r +2 = 0
$$
$$
2y''(t) + 5y'(t) + 2y(t) = 0
$$
«
Last Edit: October 12, 2018, 06:55:18 PM by Keyue Xie
»
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Yunqi(Yuki) Huang
Jr. Member
Posts: 11
Karma: 5
Re: Q3 TUT 0301
«
Reply #3 on:
October 12, 2018, 06:49:55 PM »
$$
r=-\frac{1}{2}or-2
$$
$$
(r+\frac{1}{2})(r+2) = 0
$$
$$
r^2+ 2r+\frac{1}2r +1 = 0
$$
$$
r^2+\frac{5}{2}r+1 = 0
$$
$$
2r^2 + 5r +2 = 0
$$
Therefore
$$
2y'' + 5y' + 2y = 0
$$
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Victor Ivrii
Administrator
Elder Member
Posts: 2607
Karma: 0
Re: Q3 TUT 0301
«
Reply #4 on:
October 12, 2018, 07:44:17 PM »
Yuki, only ASCII file names!
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Q3 TUT 0301