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Consider the First-Order Homogeneous System of Linear Differential Equations $\mathbf{x}(t)=C_{1}\left(\begin{array}{l}-25 \\ -16\end{array}\right) e^{-25 t}+C_{2}\left(\begin{array}{l}16 \\ -25\end{array}\right) e^{-16 t}$

Question 39

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

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