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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b1c1217-3ca9-48af-b155-11a2efe4ee10%2F8b2e9cf3-24e1-47c9-a428-ddf822c0ba37%2Fa3zi64d_processed.png&w=3840&q=75)
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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