Consider the initial value problem y' + 3y (b) Solve your equation for Y. Y = L {y} = y = 11 0 (a) Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y by Y. Do not move any terms from one side of the equation to the other (until you get to part (b) below). = if 0 < t < 1 if 1 < t < 6 if 6 < t <∞, y(0) = 10. (c) Take the inverse Laplace transform of both sides of the previous equation to solve for y.
Consider the initial value problem y' + 3y (b) Solve your equation for Y. Y = L {y} = y = 11 0 (a) Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y by Y. Do not move any terms from one side of the equation to the other (until you get to part (b) below). = if 0 < t < 1 if 1 < t < 6 if 6 < t <∞, y(0) = 10. (c) Take the inverse Laplace transform of both sides of the previous equation to solve for y.
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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Transcribed Image Text:Consider the initial value problem
y' + 3y =
(b) Solve your equation for Y.
Y = L {y}
0
11
0
(a) Take the Laplace transform of both sides of the given differential equation to create the
corresponding algebraic equation. Denote the Laplace transform of y by Y. Do not move any
terms from one side of the equation to the other (until you get to part (b) below).
=
y =
if 0 < t < 1
if 1 < t < 6
if 6 < t <∞,
y(0) = 10.
=
(c) Take the inverse Laplace transform of both sides of the previous equation to solve for y.
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