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в2 29. у" + у %3D0; У (0) — 0, У(0) — 1, у"(0) — 2

в2 29. у" + у %3D0; У (0) — 0, У(0) — 1, у"(0) — 2

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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Question 29.
In each of Problems 29 through 36, find the solution of the given initial value problem, and plot its graph. How does the solution behave as \( t \to \infty \)? 29. \( y''' + y' = 0; \quad y(0) = 0, \quad y'(0) = 1, \quad y''(0) = 2 \) 30. \( y^{(4)} + y = 0; \quad y(0) = 0, \quad y'(0) = 0, \quad y''(0) = -1, \quad y'''(0) = 0 \) 31. \( y^{(4)} - 4y''' + 4y'' = 0; \quad y(1) = -1, \quad y'(1) = 2, \quad y''(1) = 0, \quad y'''(1) = 0 \) 32. \( y''' - y'' + y' - y = 0; \quad y(0) = 2, \quad y'(0) = -1, \quad y''(0) = -2 \) 33. \( 2y^{(4)} - y''' - 9y'' + 4y' + 4y = 0; \quad y(0) = -2, \quad y'(0) = 0, \quad y''(0) = -2, \quad y'''(0) = 0 \) 34. \( 4y''' + y' + 5y = 0; \quad y(0) = 2, \quad y'(0) = 1, \quad y''(0) = -1 \) 35. \( 6y''' + 5y' + y' = 0; \quad y(0) = -2, \quad y'(0) = 2, \quad y''(0) = 0 \) 36. \( y^{(4)} + 6y''' + 17y'' + 22y' + 14y = 0; \quad y(0) = 1, \quad y'(0) = -2, \quad y''(0) = 0, \quad y'''(0) =
Transcribed Image Text:In each of Problems 29 through 36, find the solution of the given initial value problem, and plot its graph. How does the solution behave as \( t \to \infty \)? 29. \( y''' + y' = 0; \quad y(0) = 0, \quad y'(0) = 1, \quad y''(0) = 2 \) 30. \( y^{(4)} + y = 0; \quad y(0) = 0, \quad y'(0) = 0, \quad y''(0) = -1, \quad y'''(0) = 0 \) 31. \( y^{(4)} - 4y''' + 4y'' = 0; \quad y(1) = -1, \quad y'(1) = 2, \quad y''(1) = 0, \quad y'''(1) = 0 \) 32. \( y''' - y'' + y' - y = 0; \quad y(0) = 2, \quad y'(0) = -1, \quad y''(0) = -2 \) 33. \( 2y^{(4)} - y''' - 9y'' + 4y' + 4y = 0; \quad y(0) = -2, \quad y'(0) = 0, \quad y''(0) = -2, \quad y'''(0) = 0 \) 34. \( 4y''' + y' + 5y = 0; \quad y(0) = 2, \quad y'(0) = 1, \quad y''(0) = -1 \) 35. \( 6y''' + 5y' + y' = 0; \quad y(0) = -2, \quad y'(0) = 2, \quad y''(0) = 0 \) 36. \( y^{(4)} + 6y''' + 17y'' + 22y' + 14y = 0; \quad y(0) = 1, \quad y'(0) = -2, \quad y''(0) = 0, \quad y'''(0) =
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