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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, y'(π/4) = 1 4. y" + 2y + 2y = 0, y(0) = 3, y'(0) = -1 5. 9y"+y = 0, y(л/2) = 4, y'(π/2) = 0 6. 2y" - 2y + y = 0, y(-) = 1, y'(-) = -1

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, y'(π/4) = 1 4. y" + 2y + 2y = 0, y(0) = 3, y'(0) = -1 5. 9y"+y = 0, y(л/2) = 4, y'(π/2) = 0 6. 2y" - 2y + y = 0, y(-) = 1, y'(-) = -1

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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TER 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, y'(π/4) = 1 4. y" + 2y + 2y = 0, y(0) = 3, y'(0) = -1 5. 9y"+y = 0, y(π/2) = 4, y'(π/2) = 0 6. 2y" - 2y + y = 0, y(-) = 1, y'(-) = -1 7. y" + y + y = 0, y(0) = -2, y'(0) = -2 8. y" + 4y + 5y = 0, y(π/2) = 1/2, y'(π/2) = -2 nigh y(3n) = 0, y'(3л) = 1/3 9. 9y" + 6y' + 2y = 0, 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) = - Exercises 13-21: The function y(t) is a solution of the initial value problem y" + ay' + by = 0, y(t): y' (to) = yo, where the point to is specified. Determine the constants a, b, yo, and yo. 13. y(t) = sint -√2 cost, to = n/4 14. y(t) = 2 sin 2t + cos2t, to = π/4
Transcribed Image Text:TER 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, y'(π/4) = 1 4. y" + 2y + 2y = 0, y(0) = 3, y'(0) = -1 5. 9y"+y = 0, y(π/2) = 4, y'(π/2) = 0 6. 2y" - 2y + y = 0, y(-) = 1, y'(-) = -1 7. y" + y + y = 0, y(0) = -2, y'(0) = -2 8. y" + 4y + 5y = 0, y(π/2) = 1/2, y'(π/2) = -2 nigh y(3n) = 0, y'(3л) = 1/3 9. 9y" + 6y' + 2y = 0, 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) = - Exercises 13-21: The function y(t) is a solution of the initial value problem y" + ay' + by = 0, y(t): y' (to) = yo, where the point to is specified. Determine the constants a, b, yo, and yo. 13. y(t) = sint -√2 cost, to = n/4 14. y(t) = 2 sin 2t + cos2t, to = π/4
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