Solve the following initial value problem -y" + 3y - 2y = te¯t, 1 3 e 5 36 5 36 5 36 e -t e -t -t 6 e 6 6 y(0) = 0 and y' (0) = -2. e-t2 6 9 + + 9 4 9 9 4 t e t - - - 1 2t e 19 9 19 9 e 91 9 e 4t 2t e -2t

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve the following initial value problem
-y" + 3y - 2y = te-t,
1
3
5
LO
5
36
e
36
e
5
36
-e
t
e
-
e
6
y(0) = 0 and y' (0)
9
t
+ eº
е
4
e-tt
6
e-tt
6
e-tt2
6
+
+
+
9
9
4
e
9
·e`
4
e
1 2t
·e
9
19
9
19
9
91
9
2t
4t
e
e
- 2t
= -2.
Transcribed Image Text:Solve the following initial value problem -y" + 3y - 2y = te-t, 1 3 5 LO 5 36 e 36 e 5 36 -e t e - e 6 y(0) = 0 and y' (0) 9 t + eº е 4 e-tt 6 e-tt 6 e-tt2 6 + + + 9 9 4 e 9 ·e` 4 e 1 2t ·e 9 19 9 19 9 91 9 2t 4t e e - 2t = -2.
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