A system is of the form vec(X′)=Avec(X) + vec(f(t)); the fundamental matrix is: Theta = {(e2t, e-3t), (2e2t, e-3t)} and the particular solution is: xp = {(e-2tcos(t)), (e-2tsin(t))}. Find the general solution to the system, vec(X(t)). If the initial value of the system is vec(x(0)) = {(3), (4)}, find the solution to the IVP.
A system is of the form vec(X′)=Avec(X) + vec(f(t)); the fundamental matrix is: Theta = {(e2t, e-3t), (2e2t, e-3t)} and the particular solution is: xp = {(e-2tcos(t)), (e-2tsin(t))}. Find the general solution to the system, vec(X(t)). If the initial value of the system is vec(x(0)) = {(3), (4)}, find the solution to the IVP.
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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A system is of the form vec(X′)=Avec(X) + vec(f(t)); the fundamental matrix is:
Theta = {(e2t, e-3t), (2e2t, e-3t)} and the particular solution is:
xp = {(e-2tcos(t)), (e-2tsin(t))}.
Find the general solution to the system, vec(X(t)).
If the initial value of the system is vec(x(0)) = {(3), (4)}, find the solution to the IVP.
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