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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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
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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