Differential Equations

Free Version

Upgrade subject to access all content

Easy

Finding Solution to the System of Differential Equations 9

DIFFEQ-GAXJP1

What is the general solution to the linear system:

$$X'=\left(\begin{array}{cc} 4 & -3 \\\ 6 & -7\end{array}\right)X$$

A

$X=c_{1}\left(\begin{array}{c}3\\\ 2 \end{array}\right)e^{2t}+c_{2}\left(\begin{array}{c}1 \\\ 3 \end{array}\right)e^{-5t}$

B

$X=c_{1}\left(\begin{array}{c}3\\\ 2 \end{array}\right)e^{-5t}+c_{2}\left(\begin{array}{c}1 \\\ 3 \end{array}\right)e^{2t}$

C

$X=c_{1}\left(\begin{array}{c}3\\\ 2 \end{array}\right)e^{-2t}+c_{2}\left(\begin{array}{c}1 \\\ 3 \end{array}\right)e^{5t}$

D

$X=c_{1}\left(\begin{array}{c}3\\\ -2 \end{array}\right)e^{2t}+c_{2}\left(\begin{array}{c}1 \\\ -3 \end{array}\right)e^{-5t}$

E

None of the above