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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Transcribed Image Text: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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