y' - 4y = 8(t - 2), y(0) = 0
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
Use inverse LaPlace transformations and the Dirac Delta Function to evaluate the following Initial Value Problem:
![The equation displayed is:
\[ y' - 4y = \delta(t - 2), \quad y(0) = 0 \]
This is a first-order linear differential equation with an impulse function \(\delta(t - 2)\) on the right-hand side. The initial condition is \(y(0) = 0\).
Here, \(y'\) represents the derivative of \(y\) with respect to \(t\), and \(\delta(t - 2)\) is the Dirac delta function centered at \(t = 2\), often used to model impulses or sudden forces in systems. The problem involves finding the function \(y(t)\) that satisfies this differential equation and the given initial condition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe389a6be-22a8-4516-955c-095928c64efd%2F5be55b2b-31f7-42a4-a8c1-05148b10c33d%2Fwwjcej_processed.png&w=3840&q=75)
Transcribed Image Text:The equation displayed is:
\[ y' - 4y = \delta(t - 2), \quad y(0) = 0 \]
This is a first-order linear differential equation with an impulse function \(\delta(t - 2)\) on the right-hand side. The initial condition is \(y(0) = 0\).
Here, \(y'\) represents the derivative of \(y\) with respect to \(t\), and \(\delta(t - 2)\) is the Dirac delta function centered at \(t = 2\), often used to model impulses or sudden forces in systems. The problem involves finding the function \(y(t)\) that satisfies this differential equation and the given initial condition.
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