Solve using Laplace transforms. y" – y' + 5y = 58(t – "/6) sin t y(0) = y'(0) = 0 - %3D
Solve using Laplace transforms. y" – y' + 5y = 58(t – "/6) sin t y(0) = y'(0) = 0 - %3D
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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![**Problem Statement:**
Solve the differential equation using Laplace transforms.
\[ y'' - y' + 5y = 5 \delta \left(t - \frac{\pi}{6}\right) \sin t \]
Subject to the initial conditions:
\[ y(0) = y'(0) = 0 \]
**Explanation:**
This problem involves solving a second-order linear differential equation with constant coefficients and a non-homogeneous term involving the Dirac delta function, denoted by \( \delta(t - \pi/6) \). The solution requires the application of Laplace transforms to handle the Dirac delta function and the sinusoidal component \( \sin t \).
The initial conditions given are \( y(0) = 0 \) and \( y'(0) = 0 \), which are used to find particular solutions in the domain of Laplace-transformed functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e3a1ce7-d92d-4dd0-a136-4a5353c2db92%2Fc0e95eb0-28e5-4a41-8eb2-14bd20b9f4c2%2F4rog47f_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Solve the differential equation using Laplace transforms.
\[ y'' - y' + 5y = 5 \delta \left(t - \frac{\pi}{6}\right) \sin t \]
Subject to the initial conditions:
\[ y(0) = y'(0) = 0 \]
**Explanation:**
This problem involves solving a second-order linear differential equation with constant coefficients and a non-homogeneous term involving the Dirac delta function, denoted by \( \delta(t - \pi/6) \). The solution requires the application of Laplace transforms to handle the Dirac delta function and the sinusoidal component \( \sin t \).
The initial conditions given are \( y(0) = 0 \) and \( y'(0) = 0 \), which are used to find particular solutions in the domain of Laplace-transformed functions.
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