Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = 1² + 6e¹, y(0) = 0, y'(0) = 7 29 y = cos2t 8 Oy y = y = y = 29 10 43 40 29 10 -cos2t 43 40 43 40 -sin2t + -cos2t 29 cos2t+sin2t 10 43 40 -sin2t + 3 2 43 40 4 29 -sin2t + 29 cos2t+sin2t+ 1 4 4 3 1 + 8 4 8 4 1 4 + + 2 29 + 7 5 + 6 4 + 6 Set 5 Ser 7 Ser

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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Use the method of undetermined coefficients to solve the initial value problem.
y" + 4y = 1² + 6e¹, y(0) = 0, y'(0) = 7
O
y
=
y =
y =
y =
29
-cos2t
8
29
10
-cos2t
43
40
cos2t
29
10
43
40
-sin2t +
43
29
cos2t+sin2t
40 10 sin2t
43
40
-sin2t +
3
4
43
-sin2t +
40
1
29
cos2t+sin2t +
10
1
-
8
2
-1² +
1 1
3
29
4
8 4
+
4 4 4
7
+−²+·
29
1/²+
4
5
6
et
et
6
bin
5
+
bin
in
Transcribed Image Text:Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = 1² + 6e¹, y(0) = 0, y'(0) = 7 O y = y = y = y = 29 -cos2t 8 29 10 -cos2t 43 40 cos2t 29 10 43 40 -sin2t + 43 29 cos2t+sin2t 40 10 sin2t 43 40 -sin2t + 3 4 43 -sin2t + 40 1 29 cos2t+sin2t + 10 1 - 8 2 -1² + 1 1 3 29 4 8 4 + 4 4 4 7 +−²+· 29 1/²+ 4 5 6 et et 6 bin 5 + bin in
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