Consider the following second-order equation y" - y' - 6y = f(t) with initial condition y(0) = 3 and y′(0) = 4. Write the solution of this equation in terms of a (convolution) integral involving f Evaluate this convolution integral when f(t) := 250te-²t and find the solution.
Consider the following second-order equation y" - y' - 6y = f(t) with initial condition y(0) = 3 and y′(0) = 4. Write the solution of this equation in terms of a (convolution) integral involving f Evaluate this convolution integral when f(t) := 250te-²t and find the solution.
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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Transcribed Image Text:Consider the following second-order equation
y" — y' - 6y = f(t)
-
with initial condition y(0) = 3 and y'(0) = 4.
Write the solution of this equation in terms of a (convolution)
integral involving f
Evaluate this convolution integral when f(t) 250te
:=
-2t and
find the solution.
Now solve the same differential equation with the same f(t)
250te -2t
:=
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