17. y" + 4y' + 3y = e³t-3u₁ (t); y(0) = 0, y'(0) = 0

Linear Algebra: A Modern Introduction
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Number 17 show all work please
In Exercises 15-22, solve the initial value problems us-
ing Laplace transforms.
t,
0≤t≤ 2,
15. y' + 3y =
y = {ő
y (0) = 0
0,
t> 2
16. y' - 4y = 5tu₁ (t), y(0) = 1
17. y" + 4y' + 3y = e³t-3 u₁(t); y(0) = 0, y'(0) = 0
5e¹,
0 < t < 3,
18. y" - y =
0.
t> 3
2
Transcribed Image Text:In Exercises 15-22, solve the initial value problems us- ing Laplace transforms. t, 0≤t≤ 2, 15. y' + 3y = y = {ő y (0) = 0 0, t> 2 16. y' - 4y = 5tu₁ (t), y(0) = 1 17. y" + 4y' + 3y = e³t-3 u₁(t); y(0) = 0, y'(0) = 0 5e¹, 0 < t < 3, 18. y" - y = 0. t> 3 2
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