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Differential Equations

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General solution of $u'=Au$

DIFFEQ-CXXEJA

Find the general solution of $u'=Au$, where:

$$A=\left[\begin{array}{rr}3&2\\\ -4&-3\end{array}\right]$$

A

$u(t)=c_1\left[\begin{array}{c}-e^{t}\\\ 2e^{t}\end{array}\right]+ c_2\left[\begin{array}{r}-e^{-t}\\\ e^{-t}\end{array}\right]$

B

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

C

$u(t)=c_1\left[\begin{array}{c}-e^{-t}\\\ 2e^{-t}\end{array}\right]+ c_2\left[\begin{array}{r}-e^{t}\\\ e^{t}\end{array}\right]$

D

$u(t)=c_1\left[\begin{array}{c}e^{-t}\\\ 2e^{-t}\end{array}\right]+ c_2\left[\begin{array}{r}e^{t}\\\ e^{t}\end{array}\right]$