Use the Laplace transform to solve the following initial value problem: y"-11/ + 30y = -8et, y(0) = -1, > y (0) = -9. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. You do not need to perform partial fraction decomposition yet. L{y(t)}(s) = A B C b. Next, decompose L{y(t)} into its partial fraction decomposition: (s - a)2 a L{y(t)}(s) = c. Finally, take the inverse Laplace transform of both sides of the previous equation and solve for y(t). y(t) =

Use the Laplace transform to solve the following initial value problem: y"-11/ + 30y = -8et, y(0) = -1, > y (0) = -9. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. You do not need to perform partial fraction decomposition yet. L{y(t)}(s) = A B C b. Next, decompose L{y(t)} into its partial fraction decomposition: (s - a)2 a L{y(t)}(s) = c. Finally, take the inverse Laplace transform of both sides of the previous equation and solve for y(t). y(t) =

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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Question

Use the Laplace transform to solve the following initial value problem: y/" – 11y +30y = -8et, y(0) = –1,
> y(0) = -9.
%3D
a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic
equation and then solve for L{y(t)}.
You do not need to perform partial fraction decomposition yet.
L{y(t)}(s) =
A
В
b. Next, decompose L{y(t)} into its partial fraction decomposition:
S – a
(s – a)²
s –6'
S
-
L{y(t)}(s) =
%3/
c. Finally, take the inverse Laplace transform of both sides of the previous equation and solve for y(t).
y(t) =
%3D

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