where f(t)={ a. y(t)=1+t-e'-2(t-e¹-¹)u(t-1) b. y(t)=1+t-e¹-2(t-e¹-1)u(t-1) y(t)=e¹-1-t+(-3e¹-1+2t+1)µ(t-1) c. d. y(t)=e¹-1+(-2e¹¹+t+1)µ(t-1) +1 0 1 F(s) = 1 / +
where f(t)={ a. y(t)=1+t-e'-2(t-e¹-¹)u(t-1) b. y(t)=1+t-e¹-2(t-e¹-1)u(t-1) y(t)=e¹-1-t+(-3e¹-1+2t+1)µ(t-1) c. d. y(t)=e¹-1+(-2e¹¹+t+1)µ(t-1) +1 0 1 F(s) = 1 / +
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
18.as soon as possible please
![**Solve the following Differential Equation**
Given the differential equation \(y' = y = f(t)\) with the initial condition \(y(0) = 0\):
We have the piecewise function \(f(t)\) defined as:
\[ f(t) =
\begin{cases}
t + 1 & \text{for } 0 < t < 1 \\
t & \text{for } t > 1
\end{cases}
\]
And the Laplace Transform \(F(s)\) of the function \(f(t)\):
\[ F(s) = \frac{1}{s} + \frac{1}{s^2} - \frac{e^{-5}}{s} \]
Which of the following is the correct \(y(t)\)?
a. \( y(t) = 1 + t - e^t - 2(t - e^{-1})µ(t-1) \)
b. \( y(t) = 1 + t - e - 2(t - e^{-1})µ(t-1) \)
c. \( y(t) = e^t - 1 + t + (-3e^{-1} + 2t + 1)µ(t-1) \)
d. \( y(t) = e^t - 1 + (-2e^{-1} + t + 1)µ(t-1) \)
**Select the correct option:**
- ○ a
- ○ b
- ○ c
- ○ d](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa72e8965-bd79-4464-a740-a72095a0be2c%2Ffc830712-8688-417b-8b40-46107217e696%2Fgz9aadx_processed.png&w=3840&q=75)
Transcribed Image Text:**Solve the following Differential Equation**
Given the differential equation \(y' = y = f(t)\) with the initial condition \(y(0) = 0\):
We have the piecewise function \(f(t)\) defined as:
\[ f(t) =
\begin{cases}
t + 1 & \text{for } 0 < t < 1 \\
t & \text{for } t > 1
\end{cases}
\]
And the Laplace Transform \(F(s)\) of the function \(f(t)\):
\[ F(s) = \frac{1}{s} + \frac{1}{s^2} - \frac{e^{-5}}{s} \]
Which of the following is the correct \(y(t)\)?
a. \( y(t) = 1 + t - e^t - 2(t - e^{-1})µ(t-1) \)
b. \( y(t) = 1 + t - e - 2(t - e^{-1})µ(t-1) \)
c. \( y(t) = e^t - 1 + t + (-3e^{-1} + 2t + 1)µ(t-1) \)
d. \( y(t) = e^t - 1 + (-2e^{-1} + t + 1)µ(t-1) \)
**Select the correct option:**
- ○ a
- ○ b
- ○ c
- ○ d
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