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Use the Laplace transform to solve the given system of differential equations. dx dt dy dt x(0) = 0, y(0) = 4x - 2y + 2(t-1) = 3x - y + U(t-1) = x(t) = 8 y(t) = ( 4 è 3 4 e²t 2t 4 ) + ( 2e²(t-1)- 2e²-1 )u(t-1 X |)u(t-1

Use the Laplace transform to solve the given system of differential equations. dx dt dy dt x(0) = 0, y(0) = 4x - 2y + 2(t-1) = 3x - y + U(t-1) = x(t) = 8 y(t) = ( 4 è 3 4 e²t 2t 4 ) + ( 2e²(t-1)- 2e²-1 )u(t-1 X |)u(t-1

Advanced Engineering Mathematics
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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Use the Laplace transform to solve the given system of differential equations. dx dt dy dt = 4x - 2y + 2U (t-1) = 3x - y + U(t-1) 1 x(0) = 0, y(0) 8 = x(t) = ( |- ||_) + ( 2e²(t-¹) — 2e²-1 4 4 4-4)-( ) + ([ ])u(t-1 y(t) = 3 2t e X )u(t-1
Transcribed Image Text:Use the Laplace transform to solve the given system of differential equations. dx dt dy dt = 4x - 2y + 2U (t-1) = 3x - y + U(t-1) 1 x(0) = 0, y(0) 8 = x(t) = ( |- ||_) + ( 2e²(t-¹) — 2e²-1 4 4 4-4)-( ) + ([ ])u(t-1 y(t) = 3 2t e X )u(t-1
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