Solve the following higher order differential equation f(3) (t) f(²) (t) + 4f'(t)-4f(t) = 0, with initial conditions f(0) = 1, f'(0) = −1, ƒ(²) (0) = 1.
Solve the following higher order differential equation f(3) (t) f(²) (t) + 4f'(t)-4f(t) = 0, with initial conditions f(0) = 1, f'(0) = −1, ƒ(²) (0) = 1.
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 following higher order differential equation:
\[ f^{(3)}(t) - f^{(2)}(t) + 4f'(t) - 4f(t) = 0, \]
with the initial conditions \[ f(0) = 1, \quad f'(0) = -1, \quad f^{(2)}(0) = 1. \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F963c976c-848e-4cc8-9559-09cfbbaf2253%2F83e1d518-0f3b-4d21-9e04-ea8f30f57ed1%2Firggo4s_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Solve the following higher order differential equation:
\[ f^{(3)}(t) - f^{(2)}(t) + 4f'(t) - 4f(t) = 0, \]
with the initial conditions \[ f(0) = 1, \quad f'(0) = -1, \quad f^{(2)}(0) = 1. \]
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