Problem 3. Consider the following six differential equations (you do not need to solve these if you do not need the full solution to answer the questions below): 1. y" – 3y' – 3y = 0 2. sec(t)y' = 1/y, y(0) = 1 3. y" + 4y = 0 4. y" + 8y' + 15y = 0 5. y' + 4t³y = e-t“ 6. y" + 8y' + 15y = cos(3t) a. Which (if any) of these have periodically oscillating solutions as t → 0? b. Which (if any) of these have solutions that decay to zero as t → 0? c. Which (if any) of these have solutions that blow up (i.e. become infinitely large) as t → 0?
Problem 3. Consider the following six differential equations (you do not need to solve these if you do not need the full solution to answer the questions below): 1. y" – 3y' – 3y = 0 2. sec(t)y' = 1/y, y(0) = 1 3. y" + 4y = 0 4. y" + 8y' + 15y = 0 5. y' + 4t³y = e-t“ 6. y" + 8y' + 15y = cos(3t) a. Which (if any) of these have periodically oscillating solutions as t → 0? b. Which (if any) of these have solutions that decay to zero as t → 0? c. Which (if any) of these have solutions that blow up (i.e. become infinitely large) as t → 0?
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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Transcribed Image Text:Problem 3. Consider the following six differential equations (you do not need to solve these if you
do not need the full solution to answer the questions below):
1. y" – 3y' – 3y = 0
2. sec(t)y' = 1/y,
y(0) = 1
3. y" + 4y = 0
4. y" + 8y' + 15y = 0
5. y' + 4t³y = e=tt
6. y" + 8y' + 15y = cos(3t)
a. Which (if any) of these have periodically oscillating solutions as t → o?
b. Which (if any) of these have solutions that decay to zero as t → o?
c. Which (if any) of these have solutions that blow up (i.e. become infinitely large) as
t → 0?
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