(5) Solve the initial value problem y”" + y = f(t); y(0) = 0, y′(0) = 1 where 1 if 0 < t < π/2 -{" = 0 if t > π/2 f(t) =
(5) Solve the initial value problem y”" + y = f(t); y(0) = 0, y′(0) = 1 where 1 if 0 < t < π/2 -{" = 0 if t > π/2 f(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
![### Problem 5: Solve the Initial Value Problem
Solve the initial value problem given by the differential equation:
\[ y'' + y = f(t) \]
with initial conditions:
\[ y(0) = 0, \quad y'(0) = 1 \]
where the function \( f(t) \) is defined as:
\[
f(t) = \begin{cases}
1 & \text{if } 0 \le t < \frac{\pi}{2} \\
0 & \text{if } t \ge \frac{\pi}{2}
\end{cases}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb04829d0-4645-426e-bf1a-7ada40b0786f%2Fc5631c44-fdb0-4cf3-ad00-516549216938%2F8f2ln7m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 5: Solve the Initial Value Problem
Solve the initial value problem given by the differential equation:
\[ y'' + y = f(t) \]
with initial conditions:
\[ y(0) = 0, \quad y'(0) = 1 \]
where the function \( f(t) \) is defined as:
\[
f(t) = \begin{cases}
1 & \text{if } 0 \le t < \frac{\pi}{2} \\
0 & \text{if } t \ge \frac{\pi}{2}
\end{cases}
\]
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