Consider the IVP r"(t) + = e-az(), r(0) = ro, r (0) = 0, where ro > 0, a > 0. (a) Solve the above IVP mumerically and show the trajectories r(t) for various parameters To >0 and a >0. (b) Show that the above IVP admits only periodic solutions.

Consider the IVP r"(t) + = e-az(), r(0) = ro, r (0) = 0, where ro > 0, a > 0. (a) Solve the above IVP mumerically and show the trajectories r(t) for various parameters To >0 and a >0. (b) Show that the above IVP admits only periodic solutions.

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

Consider the IVP x
00(t) + x = e
−αx(t)
, x(0) = x0, x
0
(0) = 0, where x0 > 0,
α > 0.
(a) Solve the above IVP numerically and show the trajectories x(t) for various parameters
x0 > 0 and α > 0.
(b) Show that the above IVP admits only periodic solutions.

Consider the IVP r"(t) + = e-az(), r(0) = ro, r'(0) = 0, where ro > 0,
%3D
a >0.
(a) Solve the above IVP numerically and show the trajectories r(t) for various parameters
To > 0 and a > 0.
(b) Show that the above IVP admits only periodic solutions.

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