1. Find the general solution of the given differential equation using MUC: y(4) - 4y(3) – 21y(2) + 104y(1) – 80y = x² e2x + 3 – 5 cos 3x. Find its particular solution: а. Ур x²e2x xe2x 151e2x 3 b. Ур - x?e-2x -2x xe-2x 7e 3 28 98 19 cos(3x) 2744 80 324 486 1 21 5832 40 sin(3x) - 4250 725 sin(3x) x?e2x d. yp = cos(3x) 2900 2125 x?e2x xe2x 151e2x С. Ур xe2x 7e2x 3 28 98 3 cos(3x) 2744 80 1 324 486 5832 40 sin(3x) + 2900 3 sin(3x) sin(3x) - 725 cos(3x) 2900 725
1. Find the general solution of the given differential equation using MUC: y(4) - 4y(3) – 21y(2) + 104y(1) – 80y = x² e2x + 3 – 5 cos 3x. Find its particular solution: а. Ур x²e2x xe2x 151e2x 3 b. Ур - x?e-2x -2x xe-2x 7e 3 28 98 19 cos(3x) 2744 80 324 486 1 21 5832 40 sin(3x) - 4250 725 sin(3x) x?e2x d. yp = cos(3x) 2900 2125 x?e2x xe2x 151e2x С. Ур xe2x 7e2x 3 28 98 3 cos(3x) 2744 80 1 324 486 5832 40 sin(3x) + 2900 3 sin(3x) sin(3x) - 725 cos(3x) 2900 725
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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Transcribed Image Text:1. Find the general solution of the given differential equation using MUC:
y(4) - 4y(3) – 21y(2) + 104y(1) – 80y = x² e2x + 3 – 5 cos 3x.
Find its particular solution:
x²e2x
xe2x
151e2x
3
а. Ур
b. Ур
x'e-2x
xe-2x
7e
-2x
3
28
98
19
cos(3x)
2744
80
324
486
1
21
5832
40
sin(3x) -
2125
725 sin(3x)
x²e2x
d. yp =
4250
cos(3x)
2900
С. Ур
x'e2x
xe2x
151e2x
3
xe2x
+
486
7e2x
3
28
98
3
sin(3x) +
725
2744
80
324
1
5832
40
3
cos(3x)
1
sin(3x) –
725
cos(3x)
2900
2900
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