Find the solution to the given differential equation. If initial conditions are not given, find the general solution. Assume r is the independent variable. 1. 4y" +12y' +9y = 0
Find the solution to the given differential equation. If initial conditions are not given, find the general solution. Assume r is the independent variable. 1. 4y" +12y' +9y = 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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Question
![Find the solution to the given differential equation. If initial conditions are not given,
find the general solution. Assume x is the independent variable.
1. 4y" +12y' +9y = 0
2. 9y" + 6y + y = 0
3. y" + 4y + 4y = 0, y(0) = 3, y'(0) = -4
4. 9y" - 12y + 4y = 0,
y(0) = 2,
y'(0) = -1
5. y" - 6y' +9y = 0,
6. 4y" + 4y + y = 0,
7. y" - y' +0.25y = 0,
8. y" - 4y + 4y = 0,
9. y" + 2y + y = 0,
10. 9y" + 6y + y = 0,
y(0) = 0,
y(0) = -1,
y(0) = 2,
y(0) = 2,
y(0) = -3,
y(0) = 1,
y′(0) = 2
y'(0) = 2
y'(0) = -3
y'(0) = 1
y'(0) = 1
y'(0) = 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb31f8ea0-69b5-470b-9137-d0266a4565ac%2F66b15dce-26b1-4e76-a163-d42a1e510725%2Fyrb8lin_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the solution to the given differential equation. If initial conditions are not given,
find the general solution. Assume x is the independent variable.
1. 4y" +12y' +9y = 0
2. 9y" + 6y + y = 0
3. y" + 4y + 4y = 0, y(0) = 3, y'(0) = -4
4. 9y" - 12y + 4y = 0,
y(0) = 2,
y'(0) = -1
5. y" - 6y' +9y = 0,
6. 4y" + 4y + y = 0,
7. y" - y' +0.25y = 0,
8. y" - 4y + 4y = 0,
9. y" + 2y + y = 0,
10. 9y" + 6y + y = 0,
y(0) = 0,
y(0) = -1,
y(0) = 2,
y(0) = 2,
y(0) = -3,
y(0) = 1,
y′(0) = 2
y'(0) = 2
y'(0) = -3
y'(0) = 1
y'(0) = 1
y'(0) = 2
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