4) Use Laplace tranform to soluve ost<. y+y=76), cwhere fc) = Scosat, tzĘ こ
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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4) WHEN ANSWERING THE QUESTION PLEASE BE REALLY CLEAR ON EACH STEP AND USE TEXT(KEYBOARD NOT HANDWRITING) TO SHOW THE WORK IF POSSIBLE SINCE IS EASIER TO UNDERSTAND. AGAIN, BE CAREFUL ANSWERING, THANKS.
ADDITIONAL INFORMATION FOR THIS QUESTION,
Y=(0)=0
![**Problem 4: Laplace Transform Application**
Use the Laplace transform to solve the differential equation:
\[ y' + y = f(t), \]
where the function \( f(t) \) is defined as:
\[
f(t) =
\begin{cases}
0, & 0 \leq t < \frac{\pi}{2} \\
\cos t, & t \geq \frac{\pi}{2}
\end{cases}
\]
This piecewise function \( f(t) \) indicates that for the interval \( 0 \leq t < \frac{\pi}{2} \), the function's value is zero. For \( t \geq \frac{\pi}{2} \), the function's value is \( \cos t \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1f02723-d9e1-4704-83ab-f90dc08f102d%2Ff171c953-02b7-42f5-be6c-032b5bb8c1d5%2Fv5mx5fm_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 4: Laplace Transform Application**
Use the Laplace transform to solve the differential equation:
\[ y' + y = f(t), \]
where the function \( f(t) \) is defined as:
\[
f(t) =
\begin{cases}
0, & 0 \leq t < \frac{\pi}{2} \\
\cos t, & t \geq \frac{\pi}{2}
\end{cases}
\]
This piecewise function \( f(t) \) indicates that for the interval \( 0 \leq t < \frac{\pi}{2} \), the function's value is zero. For \( t \geq \frac{\pi}{2} \), the function's value is \( \cos t \).
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