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Differential Equations

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Moderate

Linear Systems - IVP of Array

DIFFEQ-CCYLN4

Solve the IVP:

$$u'=Au,u(0)=u^{(0)}$$

...where:

$$A=\left[\begin{array}{rrr}-3&0&1\\\ 0&-2&0\\\ 1&0&-3\end{array}\right],\ u^{(0)}=\left[\begin{array}{r}1\\\ 2\\\ 3\end{array}\right]$$

A

$u(t)=\left[\begin{array}{c}e^{-4t}+2e^{-2t}\\\ 2e^{-2t}\\\ -e^{-4t}+2e^{-2t}\end{array}\right]$

B

$u(t)=\left[\begin{array}{c}-e^{-4t}+2e^{-2t}\\\ 2e^{-2t}\\\ e^{-4t}+2e^{-2t}\end{array}\right]$

C

$u(t)=\left[\begin{array}{c}2e^{-2t}\\\ -e^{-4t}+2e^{-2t}\\\ e^{-4t}+2e^{-2t}\end{array}\right]$

D

$u(t)=\left[\begin{array}{c}-e^{-4t}\\\ 2e^{-2t}\\\ e^{-4t}\end{array}\right]$