7.6 Problems Solve the initial value problems in Problems 1 through 8, and graph each solution function x(t). 1. x" + 4x 2. x" + 4x = 8(1) + 8(t – 1); x(0) = x'(0) = 0 3. x" + 4x' + 4x = 1 + 8(t – 2); x(0) = x'(0) = 0 4. x" + 2x' + x = t + 8(t); x (0) = 0, x'(0) = 1 5. x" + 2x' + 2x = 8(t); x(0) = x'(0) = 0 = %3D %3| 28(t – 1); x(0) = x'(0) = 0 %3D 6. x" + 9x = 8(t – 3n) + cos 3t; x (0) = x'(0) = 0 7. x" + 4x' +5x = 8(t – x) + 8(t – 27); x(0) = 0, x' (0) = 2 8. x" + 2x' +x = 8(t) – 8(t – 2); x(0) = x'(0) = 2
7.6 Problems Solve the initial value problems in Problems 1 through 8, and graph each solution function x(t). 1. x" + 4x 2. x" + 4x = 8(1) + 8(t – 1); x(0) = x'(0) = 0 3. x" + 4x' + 4x = 1 + 8(t – 2); x(0) = x'(0) = 0 4. x" + 2x' + x = t + 8(t); x (0) = 0, x'(0) = 1 5. x" + 2x' + 2x = 8(t); x(0) = x'(0) = 0 = %3D %3| 28(t – 1); x(0) = x'(0) = 0 %3D 6. x" + 9x = 8(t – 3n) + cos 3t; x (0) = x'(0) = 0 7. x" + 4x' +5x = 8(t – x) + 8(t – 27); x(0) = 0, x' (0) = 2 8. x" + 2x' +x = 8(t) – 8(t – 2); x(0) = x'(0) = 2
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 solve #7
Transcribed Image Text:7.6 Problems
Solve the initial value problems in Problems 1 through 8, and
graph each solution function x(t).
1. x" + 4x
2. x" + 4x = 8(1) + 8(t – 1); x(0) = x'(0) = 0
3. x" + 4x' + 4x = 1 + 8(t – 2); x(0) = x'(0) = 0
4. x" + 2x' + x = t + 8(t); x (0) = 0, x'(0) = 1
5. x" + 2x' + 2x =
8(t); x(0) = x'(0) = 0
=
%3D
%3|
28(t – 1); x(0) = x'(0) = 0
%3D
6. x" + 9x = 8(t – 3n) + cos 3t; x (0) = x'(0) = 0
7. x" + 4x' +5x = 8(t – x) + 8(t – 27); x(0) = 0, x' (0) = 2
8. x" + 2x' +x = 8(t) – 8(t – 2); x(0) = x'(0) = 2
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