Consider the following system of coupled ODES. f = fi(t) + f2(t)–2f3(t) f;(t) = -fi(t) + 2f2(t)+f3(t) f(t) = f2(t) – f3(t) 4 Where F(0) = (-4).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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4. Consider the following system of coupled ODES.
f(t) = fi(t) + fa(t)-2f3(t)
f(t) = -fi(t) + 2f2(t)+f3(t)
f(t) = f2(t) – f3(t)
4
Where F(0) = (-4).
2.
a) Rewrite the above system in matrix form and use this to find the eigenvalues and
eigenvectors of the coefficient matrix.
b) Use your solutions from above to solve the system of coupled ODES.
c) Use your solutions and the original system given in the question to check all your
solutions.
Transcribed Image Text:4. Consider the following system of coupled ODES. f(t) = fi(t) + fa(t)-2f3(t) f(t) = -fi(t) + 2f2(t)+f3(t) f(t) = f2(t) – f3(t) 4 Where F(0) = (-4). 2. a) Rewrite the above system in matrix form and use this to find the eigenvalues and eigenvectors of the coefficient matrix. b) Use your solutions from above to solve the system of coupled ODES. c) Use your solutions and the original system given in the question to check all your solutions.
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