Consider the first-order homogeneous system of linear differential equations = x
Which of these is the genreal solution of the system? Here, and are arbitrary real constants.
A) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}-25 \ -16\end{array}\right) e^{-25 t}+C_{2}\left(\begin{array}{l}16 \ -25\end{array}\right) e^{-16 t} $
B) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}-16 \ -25\end{array}\right) e^{25 t}+C_{2}\left(\begin{array}{c}16 \ -25\end{array}\right) e^{-16 t} $
C) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}5 \mathrm{i} \ 4 \mathrm{i}\end{array}\right) e^{20 t}+C_{2}\left(\begin{array}{c}-5 \mathrm{i} \ 4 \mathrm{i}\end{array}\right) e^{-20 t} $
D) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}-16 \ -25\end{array}\right) e^{25 t}+C_{2}\left(\begin{array}{c}16 \ -25\end{array}\right) e^{16 t} $
E) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}5 \mathrm{i} \ 4 \mathrm{i}\end{array}\right) e^{-20 t}+C_{2}\left(\begin{array}{c}-5 \mathrm{i} \ 4 \mathrm{i}\end{array}\right) e^{20 t} $

Question

Consider the first-order homogeneous system of linear differential equations  =  x
Which of these is the genreal solution of the system? Here,  and  are arbitrary real constants.
A) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}-25 \ -16\end{array}\right) e^{-25 t}+C_{2}\left(\begin{array}{l}16 \ -25\end{array}\right) e^{-16 t} $ 
B) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}-16 \ -25\end{array}\right) e^{25 t}+C_{2}\left(\begin{array}{c}16 \ -25\end{array}\right) e^{-16 t} $ 
C) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}5 \mathrm{i} \ 4 \mathrm{i}\end{array}\right) e^{20 t}+C_{2}\left(\begin{array}{c}-5 \mathrm{i} \ 4 \mathrm{i}\end{array}\right) e^{-20 t} $ 
D) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}-16 \ -25\end{array}\right) e^{25 t}+C_{2}\left(\begin{array}{c}16 \ -25\end{array}\right) e^{16 t} $ 
E) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}5 \mathrm{i} \ 4 \mathrm{i}\end{array}\right) e^{-20 t}+C_{2}\left(\begin{array}{c}-5 \mathrm{i} \ 4 \mathrm{i}\end{array}\right) e^{20 t} $

Quizplus · Accepted Answer

The Answer of Consider the first-order homogeneous system of linear differential equations  =  x
Which of these is the genreal solution of the system? Here,  and  are arbitrary real constants.
A) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}-25 \ -16\end{array}\right) e^{-25 t}+C_{2}\left(\begin{array}{l}16 \ -25\end{array}\right) e^{-16 t} $ 
B) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}-16 \ -25\end{array}\right) e^{25 t}+C_{2}\left(\begin{array}{c}16 \ -25\end{array}\right) e^{-16 t} $ 
C) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}5 \mathrm{i} \ 4 \mathrm{i}\end{array}\right) e^{20 t}+C_{2}\left(\begin{array}{c}-5 \mathrm{i} \ 4 \mathrm{i}\end{array}\right) e^{-20 t} $ 
D) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}-16 \ -25\end{array}\right) e^{25 t}+C_{2}\left(\begin{array}{c}16 \ -25\end{array}\right) e^{16 t} $ 
E) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}5 \mathrm{i} \ 4 \mathrm{i}\end{array}\right) e^{-20 t}+C_{2}\left(\begin{array}{c}-5 \mathrm{i} \ 4 \mathrm{i}\end{array}\right) e^{20 t} $