der the system of ODEs below: 4y₁ + 4y2 -2y₁ + e²t Show that the complementary solution to the given system is: V₁,c = C₁e²t cos 2t + C₂e²t sin 2t Y2,c = C₁e²t (- cos 2t - sin2t) + C₂e²t (cos 2t - sin 2t)
der the system of ODEs below: 4y₁ + 4y2 -2y₁ + e²t Show that the complementary solution to the given system is: V₁,c = C₁e²t cos 2t + C₂e²t sin 2t Y2,c = C₁e²t (- cos 2t - sin2t) + C₂e²t (cos 2t - sin 2t)
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 system of ODEs below:
y₁ = 4y₁ + 4y₂
y2 = -2y₁ + e²t
1. Show that the complementary solution to the given system is:
V₁,c = C₁e²t cos 2t + C₂e²t sin 2t
V2,c = C₁e²t (- cos 2t - sin2t) + C₂e2t (cos 2t - sin 2t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87be90e1-f97b-4bdf-a1f1-e9d4767e5e2c%2F0e0c1233-74c4-4284-987a-b1a2f80fa563%2Fcno91gw_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the system of ODEs below:
y₁ = 4y₁ + 4y₂
y2 = -2y₁ + e²t
1. Show that the complementary solution to the given system is:
V₁,c = C₁e²t cos 2t + C₂e²t sin 2t
V2,c = C₁e²t (- cos 2t - sin2t) + C₂e2t (cos 2t - sin 2t)
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