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Differential Equations

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Difficult

Linear System with Repeated E-value: A Component

DIFFEQ-Y$RMNT

Consider the following system of equations:

$$ \left\{\begin{array}{c} x_1'-3x_1+4x_2=0\\\ x_2'-x_1+x_2=0 \end{array} \right. $$

with the initial conditions $x_1(0)=1, x_2(0)=2$. Then, the function $x_2(t)$ is

A

$2e^t-3te^t$

B

$e^t-6te^t$

C

$2e^t$

D

$e^t$