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1. Find the general solution of the following differential equations. a) x"" + x = 0. b) x + x = 1. c) x² + x² = 0. d) x'"- x' - 8x = 0. e) x""+x" = 2et + 3t². f) x"" - 8x = 0.

1. Find the general solution of the following differential equations. a) x"" + x = 0. b) x + x = 1. c) x² + x² = 0. d) x'"- x' - 8x = 0. e) x""+x" = 2et + 3t². f) x"" - 8x = 0.

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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2nd 106 (N 130 T DRG N DEL (k a) x²" + x = 0. b) x + x = 1. c) x + x = 0. 1401 TEN EXERCISES 1. Find the general solution of the following differential equations. 2.6 Steadu A A ( a 2. Second-Order Linear Equations 4. d) x"" - x' - 8x = 0. e) x"" + x = 2e +3t². f) x"" - 8x = 0. - 2. Solve the initial value problem x"" +x" - 4x' - 4x = 0, x(0) = 1, x'(0)= x" (0) = -1. Hint: Guess one eigenvalue. 3. Write a linear, fourth-order differential equation whose general solution x(t) = C₁ + c₂t+e5t (c4 cos 2t + c5 sin 5t). 4. What is the general solution of a fourth-order differential equation i four eigenvalues are λ = 3±i, 3i? What is the differential equatio
Transcribed Image Text:2nd 106 (N 130 T DRG N DEL (k a) x²" + x = 0. b) x + x = 1. c) x + x = 0. 1401 TEN EXERCISES 1. Find the general solution of the following differential equations. 2.6 Steadu A A ( a 2. Second-Order Linear Equations 4. d) x"" - x' - 8x = 0. e) x"" + x = 2e +3t². f) x"" - 8x = 0. - 2. Solve the initial value problem x"" +x" - 4x' - 4x = 0, x(0) = 1, x'(0)= x" (0) = -1. Hint: Guess one eigenvalue. 3. Write a linear, fourth-order differential equation whose general solution x(t) = C₁ + c₂t+e5t (c4 cos 2t + c5 sin 5t). 4. What is the general solution of a fourth-order differential equation i four eigenvalues are λ = 3±i, 3i? What is the differential equatio
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