Exercises 1-15: (a) Find the general solution of the differential equation. (b) Impose the initial conditions to obtain the unique solution of the initial value prob- lem. (c) Describe the behavior of the solution y(t) as t → -o and as t → o. Does y(t) ap- proach -00, +0, or a finite limit? 1. y" + y - 2y = 0, y(0) = 3, y'(0) = -3 2. y" – y = 0, y(2) = 1, y (2) = 0 3. y" – 4y' + 3y = 0, y(0) = -1, y'(0) = 1 4. 2y" – 5y' + 2y = 0, y(0) = -1, y'(0) = -5 5. y" – y = 0, y(0) = 1, y (0) = -1
Exercises 1-15: (a) Find the general solution of the differential equation. (b) Impose the initial conditions to obtain the unique solution of the initial value prob- lem. (c) Describe the behavior of the solution y(t) as t → -o and as t → o. Does y(t) ap- proach -00, +0, or a finite limit? 1. y" + y - 2y = 0, y(0) = 3, y'(0) = -3 2. y" – y = 0, y(2) = 1, y (2) = 0 3. y" – 4y' + 3y = 0, y(0) = -1, y'(0) = 1 4. 2y" – 5y' + 2y = 0, y(0) = -1, y'(0) = -5 5. y" – y = 0, y(0) = 1, y (0) = -1
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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Question
Please answer #5
section 3.3
Transcribed Image Text:Exercises 1-15:
(a) Find the general solution of the differential equation.
(b) Impose the initial conditions to obtain the unique solution of the initial value prob-
lem.
(c) Describe the behavior of the solution y(t) as t → -o and as t → o. Does y(t) ap-
proach -00, +0, or a finite limit?
1. у" + у — 2у %3D0, у(0) %3 3, У (0) %3D — 3
2. y" – ty = 0, y(2) = 1, y (2) = 0
3. y" – 4y' + 3y = 0, y(0) = -1, y'(0) = 1
4. 2y" – 5y' + 2y = 0, y(0) = -1, y'(0) = -5
5. y" – y = 0, y(0) = 1, y (0) =-1
6. y" + 2y' = 0, y(-1) = 0, y(-1) = 2
7. y" + 5y' + 6y = 0, y(0) = 1, y'(0) = -1
8. у" - 5у' + бу %3D 0, у(0) 3 1, у'(0) 3 -1
%3D
9. y" – 4y = 0, y(3) = 0, y'(3) = 0
10. 8y" - бу' + у%3D 0, у(1) %3D 4, У(1) %3D3
11. 2y"- Зу' — 0, У(-2) — 3, У(-2) — 0
y(-2) = 0
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