Select the best answer to each question. In your solution sheet, write t the correct answer. If your answer is not among the options, write the 1. Find using Method of Undetermined Coefficient (MUC):

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10th Edition
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Select the best answer to each question. In your solution sheet, write the letter of
the correct answer. If your answer is not among the options, write the letter 'E'.
1. Find using Method of Undetermined Coefficient (MUC):
y(4) – y(3) – y(2) + y(1) = xe¬2* – 10x? + 8 cos(2x).
a. Find its general solution of the homogeneous equation:
b. yc = c1 + Cze¯* + e¬*(c3 cos(x) +
C4 sin(x)
d. Yc = C1 + Cze¯* + e*(c3 cos(x) +
C4 sin(x)
a. Yc = C1 + c2xe¯* + c3e* + C4xe*
C. Yc = C1e* + c2xe¯* + C3e* + C4xe*
b. Find its particular solution:
10x3
+
e-2*
5x3
13
+
108
e-2x
13
5x2 –
-2x
+ 10x² +
b. Ур
-2x
а. Ур
18
54
4
8
8
20х +
25
4
sin(2x) – cos(2x)
sin(2x)
cos(2x)
40x
- -
- -
- -
25
25
-2x
e
-2x
5x3
+ 5x? +
10x3
13
e-2x
108
13
10x2 –
d. Yp
-2x
с. Ур
-
18
4
40x +
25
3
9
8
54
3
4
8
sin(2x) + cos(2x)
sin(2x) +
cos(2x)
20x
25
25
c. Write your general solution here (In your solution sheet), it might give the answer
from previous questions if I post the choices
Transcribed Image Text:Select the best answer to each question. In your solution sheet, write the letter of the correct answer. If your answer is not among the options, write the letter 'E'. 1. Find using Method of Undetermined Coefficient (MUC): y(4) – y(3) – y(2) + y(1) = xe¬2* – 10x? + 8 cos(2x). a. Find its general solution of the homogeneous equation: b. yc = c1 + Cze¯* + e¬*(c3 cos(x) + C4 sin(x) d. Yc = C1 + Cze¯* + e*(c3 cos(x) + C4 sin(x) a. Yc = C1 + c2xe¯* + c3e* + C4xe* C. Yc = C1e* + c2xe¯* + C3e* + C4xe* b. Find its particular solution: 10x3 + e-2* 5x3 13 + 108 e-2x 13 5x2 – -2x + 10x² + b. Ур -2x а. Ур 18 54 4 8 8 20х + 25 4 sin(2x) – cos(2x) sin(2x) cos(2x) 40x - - - - - - 25 25 -2x e -2x 5x3 + 5x? + 10x3 13 e-2x 108 13 10x2 – d. Yp -2x с. Ур - 18 4 40x + 25 3 9 8 54 3 4 8 sin(2x) + cos(2x) sin(2x) + cos(2x) 20x 25 25 c. Write your general solution here (In your solution sheet), it might give the answer from previous questions if I post the choices
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