3. Convert the following higher-order equations to systems of first-order equa-tions.NUMERICAL METHODS FOR SYSTEMS47(a) Y"(t) + 4Y"(t) + 5Y'(t) + 2Y (t) = 2t2 + 10t + 8,Y (0) = 1, Y'(0) = -1, Y"(0) = 3.The true solution is Y (t) = e-t + t2.%3D(b) Y"(t) + 4Y'(t) + 13Y (t) = 40 cos(t),Y (0) = 3, Y'(0) = 4.The true solution is Y (t) = 3 cos(t) + sin(t) + e-2t sin(3t).

Answered: Image /qna-images/answer/f637bf32-6c64-4048-bf9b-aaa970a57058.jpg

3. Convert the following higher-order equations to systems of first-order equa- tions. NUMERICAL METHODS FOR SYSTEMS 47 2t2 + 10t + 8, (а) Ү" () + 4Y"() + 5Y'({) + 2Y (t) — Y (0) = 1, Y'(0) = -1, Y"(0) = 3. The true solution is Y (t) = e-t +t². (b) Y"(t) + 4Y'(t) + 13Y (t) = 40 cos(t), Y(0) = 3, Y'(0) = 4. The true solution is Y (t) = 3 cos(t) + sin(t) + e-2t sin(3t). %3D

3. Convert the following higher-order equations to systems of first-order equa- tions. NUMERICAL METHODS FOR SYSTEMS 47 2t2 + 10t + 8, (а) Ү" () + 4Y"() + 5Y'({) + 2Y (t) — Y (0) = 1, Y'(0) = -1, Y"(0) = 3. The true solution is Y (t) = e-t +t². (b) Y"(t) + 4Y'(t) + 13Y (t) = 40 cos(t), Y(0) = 3, Y'(0) = 4. The true solution is Y (t) = 3 cos(t) + sin(t) + e-2t sin(3t). %3D

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

3. Convert the following higher-order equations to systems of first-order equa-
tions.
NUMERICAL METHODS FOR SYSTEMS
47
(a) Y"(t) + 4Y"(t) + 5Y'(t) + 2Y (t) = 2t2 + 10t + 8,
Y (0) = 1, Y'(0) = -1, Y"(0) = 3.
The true solution is Y (t) = e-t + t2.
%3D
(b) Y"(t) + 4Y'(t) + 13Y (t) = 40 cos(t),
Y (0) = 3, Y'(0) = 4.
The true solution is Y (t) = 3 cos(t) + sin(t) + e-2t sin(3t).

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