Consider the system of ODEs below: Jy₁ = 4y₁ + 4y2 3₂2 = -2y₁+e²t 2A. Show that the complementary solution of the given system is: 31,c = C₁e²t cos 2t + c₂e²t sin 2t Y2,c = C₁e²t (- cos 2t - sin 2t) + c₂e²t (cos 2t - sin 2t)

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Answer question 2A and show complete solution.

Consider the system of ODEs below:
Sy₁ = 4y₁ + 4y2
y/₂ = -2y₁ + e²t
2A. Show that the complementary solution of the given system is:
2t
31,c = C₁e²t cos 2t + c₂e²t sin 2t
Y2,c = C₁e²t (- cos 2t - sin 2t) + c₂e²t (cos 2t - sin 2t)
2B. Using yc above, solve for the particular solution of the system using Method of Variation of
Parameters only.
Transcribed Image Text:Consider the system of ODEs below: Sy₁ = 4y₁ + 4y2 y/₂ = -2y₁ + e²t 2A. Show that the complementary solution of the given system is: 2t 31,c = C₁e²t cos 2t + c₂e²t sin 2t Y2,c = C₁e²t (- cos 2t - sin 2t) + c₂e²t (cos 2t - sin 2t) 2B. Using yc above, solve for the particular solution of the system using Method of Variation of Parameters only.
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