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12. 9y" +²y = 0, y(3)=2, y'(3) = - Exercises 13-21:

12. 9y" +²y = 0, y(3)=2, y'(3) = - Exercises 13-21:

Advanced Engineering Mathematics
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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Please show all work and do all parts. Only do question 12.
CHAPTER 3 Second and Higher Order Linear Differential Equations Exercises 3-12: For the given differential equation, (a) Determine the roots of the characteristic equation. (b) Obtain the general solution as a linear combination of real-valued solutions. (c) Impose the initial conditions and solve the initial value problem. 3. y" + 4y = 0, y(π/4)= -2, 4. y" + 2y + 2y = 0, y(0) = 3, 5. 9y"+y = 0, 6. 2y" - 2y + y = 0, 7. y"+y' + y = 0, 8. y" + 4y + 5y = 0, 9. 9y" + 6y' + 2y = 0, y(-) = 1, y'(-) = -1 y(0) = -2, y'(0) = -2 LED to doera erT y(π/2) = 1/2, y'(π/2) = -2 right y(3л) = 0, y'(3л) = 1/3 10. y" +4n²y = 0, y(1)=2, y'(1) = 1 11. y" - 2√2y' + 3y = 0, y(0) = -1/2, y'(0) = √2 12. 9y" + ²y = 0, y(3) = 2, y'(3) = - y'(π/4) = 1 y'(0) = -1 de 1800 £ la riq y(л/2) = 4, y'(π/2) = 0 Exercises 13-21: The function y(t) is a solution of the initial value problem y" + ay' + by = 0, y(to) - Yo y' (to) = yo, where the point to is specified. Determine the constants a, b, yo, and yo. 13. y(t) = sint -√2 cost, to = π/4 14. y(t) = 2 sin 2t + cos 2t, to = π/4
Transcribed Image Text:CHAPTER 3 Second and Higher Order Linear Differential Equations Exercises 3-12: For the given differential equation, (a) Determine the roots of the characteristic equation. (b) Obtain the general solution as a linear combination of real-valued solutions. (c) Impose the initial conditions and solve the initial value problem. 3. y" + 4y = 0, y(π/4)= -2, 4. y" + 2y + 2y = 0, y(0) = 3, 5. 9y"+y = 0, 6. 2y" - 2y + y = 0, 7. y"+y' + y = 0, 8. y" + 4y + 5y = 0, 9. 9y" + 6y' + 2y = 0, y(-) = 1, y'(-) = -1 y(0) = -2, y'(0) = -2 LED to doera erT y(π/2) = 1/2, y'(π/2) = -2 right y(3л) = 0, y'(3л) = 1/3 10. y" +4n²y = 0, y(1)=2, y'(1) = 1 11. y" - 2√2y' + 3y = 0, y(0) = -1/2, y'(0) = √2 12. 9y" + ²y = 0, y(3) = 2, y'(3) = - y'(π/4) = 1 y'(0) = -1 de 1800 £ la riq y(л/2) = 4, y'(π/2) = 0 Exercises 13-21: The function y(t) is a solution of the initial value problem y" + ay' + by = 0, y(to) - Yo y' (to) = yo, where the point to is specified. Determine the constants a, b, yo, and yo. 13. y(t) = sint -√2 cost, to = π/4 14. y(t) = 2 sin 2t + cos 2t, to = π/4
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