1. The function yı = e² is a solution to (I- 1)y/" - 2ry + (x + 1)y = 0, x> 1. Use reduction of order to find a function y2 so that the pair {y1, 2} form a r set of solutions to the differential equation A. y2 = (1 - 1), B. 2 = (1 – 1)°e, C. 2 = (1- 1)2, D. 2 = (x- 1) e E. None of these. 2. Let {y1, 2} be a fundamental system of solutions for the differential equatic y'- 2xy +y = 0. If the Wronskian satisfies Wy1, 42](0) = 1, then W[y1, 2](x) is equa to A. e В. еа C. z2 D. -r E. None of these 3. The general solution for the DE y" - 2y-2y = 0 is A. y = c,ev3 + ge-zv3 B. y = CzeV3, C. y= ce(1+v3) +ze=(1-v3), D. y = Ce cos(z/3) + cze* sin(zv/3. E. None of these.
1. The function yı = e² is a solution to (I- 1)y/" - 2ry + (x + 1)y = 0, x> 1. Use reduction of order to find a function y2 so that the pair {y1, 2} form a r set of solutions to the differential equation A. y2 = (1 - 1), B. 2 = (1 – 1)°e, C. 2 = (1- 1)2, D. 2 = (x- 1) e E. None of these. 2. Let {y1, 2} be a fundamental system of solutions for the differential equatic y'- 2xy +y = 0. If the Wronskian satisfies Wy1, 42](0) = 1, then W[y1, 2](x) is equa to A. e В. еа C. z2 D. -r E. None of these 3. The general solution for the DE y" - 2y-2y = 0 is A. y = c,ev3 + ge-zv3 B. y = CzeV3, C. y= ce(1+v3) +ze=(1-v3), D. y = Ce cos(z/3) + cze* sin(zv/3. E. None of these.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
 = 1, then W[y1, Y2](x) is equa:
to
A. ez
B. e-z
C. 72
D. -x2
E. None of these
3.
The general solution for the DE y' – 2y' – 2y = 0 is
A. y = c,e²v3
+ cze-zv3
C. y = ce(1+v3) + cze=(1-v3),
D. y = Ce cos(r/3) + cze" sin(zv3.
E. None of these.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03eb469a-6e80-4cf7-90ca-90ee1aef0bd2%2F31c0bf16-e2f9-4c03-9b62-7151cccc4463%2Ff99qmqh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.
The function y1 = e² is a solution to
(x - 1)y" – 2ry + (x+ 1)y = 0, ¤ > 1.
Use reduction of order to find a function y2 so that the pair {y1, ¥2} form a f
set of solutions to the differential equation
A. y2 = (x – 1)³,
B. y2 = (1 – 1)³e²,
C. y2 = (x – 1)²,
D. y2 = (x – 1)²e²
E. None of these.
2.
Let {y1, 42} be a fundamental system of solutions for the differential equatic
y'
2xy + y = 0. If the Wronskian satisfies Wy1, Y2](0) = 1, then W[y1, Y2](x) is equa:
to
A. ez
B. e-z
C. 72
D. -x2
E. None of these
3.
The general solution for the DE y' – 2y' – 2y = 0 is
A. y = c,e²v3
+ cze-zv3
C. y = ce(1+v3) + cze=(1-v3),
D. y = Ce cos(r/3) + cze" sin(zv3.
E. None of these.
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