Solve the initial-value problem where f(t)= = 2: y'-y = f(t), y(0) = 1 0 ≤t≤1 t≥1 1: in the following two ways: a) Using the Laplace transform b) By directly solving the first-order linear differential equation techniques discussed in previous chapters.
Solve the initial-value problem where f(t)= = 2: y'-y = f(t), y(0) = 1 0 ≤t≤1 t≥1 1: in the following two ways: a) Using the Laplace transform b) By directly solving the first-order linear differential equation techniques discussed in previous chapters.
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
![Solve the initial-value problem:
\[ y' - y = f(t), \quad y(0) = 1 \]
where
\[
f(t) =
\begin{cases}
2; & 0 \leq t \leq 1 \\
-1; & t \geq 1
\end{cases}
\]
in the following two ways:
a) Using the Laplace transform
b) By directly solving the first-order linear differential equation techniques discussed in previous chapters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13b8e596-45c0-434d-ab2b-ea5ebc953e71%2F18d41347-210a-46d9-a1df-e137c5f3a5da%2Fpev1vpk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Solve the initial-value problem:
\[ y' - y = f(t), \quad y(0) = 1 \]
where
\[
f(t) =
\begin{cases}
2; & 0 \leq t \leq 1 \\
-1; & t \geq 1
\end{cases}
\]
in the following two ways:
a) Using the Laplace transform
b) By directly solving the first-order linear differential equation techniques discussed in previous chapters.
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