2. Find using Method of Undetermined Coefficient (MUC): y(3) – 2y(2) + y(1) = 4xe2x* – 3x2 – 4x + 2sin(3x) y'(0) = -3, y(0) = -10, y"(0) = -1 a. Find its general solution of the homogeneous equation: a. Yc = C1 + cze¬* + c3xe¬2x b. yc = c1 + Cze* + c3xe* d. yc = c1e* + e*(c2 cos(x) + Cz sin(x)) C. Yc = c1 + C2e² + cze2x

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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'.

2. Find using Method of Undetermined Coefficient (MUC):
y(3) – 2y(2) + y(1) = 4xe2x – 3x² – 4x + 2sin(3x)
у' (0) — — 3,
у (0) 3D —10,
у" (0) — —1
a. Find its general solution of the homogeneous equation:
a. Yc = C1 + Cze¬* + c3xe¯2x
b. yc = c1 + Cze* + c3xe*
d. yc = ce* + e*(c2 cos(x) +
Cz sin(x))
C. Yc = C1 + C2e? + cze2x
b. Find its particular solution:
а. у, — —х3 - 7х2 — 22х + 2e2хx +
b. yp == x³ + 4x? + 10x – 2e2xx –
50 sin(3x) + cos(3x) – 5e2x
С. У, — х3 + 5x2 + 14х — е2хx —
1
1
2
4
75
25
sin(3x) – cos(3x) + 5e2x
75
d. Yp
—х3 — 8х2 — 26х + 2е2*х +
1
25 sin(3x) - cos(3x) +e2*
25 sin (3x) +cos(3x) – 5e2x
C. Find its solution with a given initial value problem
Transcribed Image Text:2. Find using Method of Undetermined Coefficient (MUC): y(3) – 2y(2) + y(1) = 4xe2x – 3x² – 4x + 2sin(3x) у' (0) — — 3, у (0) 3D —10, у" (0) — —1 a. Find its general solution of the homogeneous equation: a. Yc = C1 + Cze¬* + c3xe¯2x b. yc = c1 + Cze* + c3xe* d. yc = ce* + e*(c2 cos(x) + Cz sin(x)) C. Yc = C1 + C2e? + cze2x b. Find its particular solution: а. у, — —х3 - 7х2 — 22х + 2e2хx + b. yp == x³ + 4x? + 10x – 2e2xx – 50 sin(3x) + cos(3x) – 5e2x С. У, — х3 + 5x2 + 14х — е2хx — 1 1 2 4 75 25 sin(3x) – cos(3x) + 5e2x 75 d. Yp —х3 — 8х2 — 26х + 2е2*х + 1 25 sin(3x) - cos(3x) +e2* 25 sin (3x) +cos(3x) – 5e2x C. Find its solution with a given initial value problem
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