olve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" + 4y = g(t), y(0) = -2, y'(0) = 0, where g(t) = t, t <3 4, t> 3 lick here to view the table of Laplace transforms. lick here to view the table of properties of Laplace transforms. *** [s) = 0 ype an exact answer in terms of e.)
olve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" + 4y = g(t), y(0) = -2, y'(0) = 0, where g(t) = t, t <3 4, t> 3 lick here to view the table of Laplace transforms. lick here to view the table of properties of Laplace transforms. *** [s) = 0 ype an exact answer in terms of e.)
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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![### Solving for Y(s), the Laplace Transform of the Solution y(t)
To solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem given below:
\[ y'' + 4y = g(t) \]
\[ y(0) = -2, \quad y'(0) = 0 \]
where
\[ g(t) =
\begin{cases}
t, & \text{if } t < 3 \\
4, & \text{if } t > 3
\end{cases}
\]
You are encouraged to use the following resources:
- [Table of Laplace Transforms](#)
- [Table of Properties of Laplace Transforms](#)
To solve the problem, input the Laplace transform \( Y(s) \) in the box below:
\[ Y(s) = \boxed{\text{(Type an exact answer in terms of } e.\text{)}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45088ba1-a1a3-4a96-b462-54f2c0a5a29e%2Fb5af74be-8f33-4e2f-a07b-fcab8ac02a00%2Fb0h40e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving for Y(s), the Laplace Transform of the Solution y(t)
To solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem given below:
\[ y'' + 4y = g(t) \]
\[ y(0) = -2, \quad y'(0) = 0 \]
where
\[ g(t) =
\begin{cases}
t, & \text{if } t < 3 \\
4, & \text{if } t > 3
\end{cases}
\]
You are encouraged to use the following resources:
- [Table of Laplace Transforms](#)
- [Table of Properties of Laplace Transforms](#)
To solve the problem, input the Laplace transform \( Y(s) \) in the box below:
\[ Y(s) = \boxed{\text{(Type an exact answer in terms of } e.\text{)}} \]
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