Consider the first-order homogeneous system of linear differential equations

What is the general solution of this system? Here, is an arbitrary constant vector.
A) $ \mathbf{x}(t)=\left(\begin{array}{lll}e^{t} & e^{4 t} & \left(t-\frac{1}{6}\right) e^{4 t} \ 6 e^{t} & -3 e^{4 t} & -3 t e^{4 t} \ 3 e^{t} & 0 & 0\end{array}\right) \mathbf{C} $
B) $ \mathbf{x}(t)=\left(\begin{array}{lll}e^{t} & e^{4 t} & \left(t+\frac{1}{6}\right) e^{4 t} \ 6 e^{t} & 3 e^{4 t} & 3 t e^{4 t} \ 3 e^{t} & 0 & 0\end{array}\right) $ C
C) $ \mathbf{x}(t)=\left[\begin{array}{lll}e^{t} & e^{4 t} & \left(t+\frac{1}{6}\right) e^{4 t} \ -3 e^{t} & -3 e^{4 t} & 3 t e^{4 t} \ 6 e^{t} & 0 & 0\end{array}\right] $ C
D) $ \mathbf{x}(t)=\left[\begin{array}{lll}e^{-t} & e^{-4 t} & \left(t+\frac{1}{6}\right) e^{-4 t} \ 6 e^{-t} & 3 e^{-4 t} & 3 t e^{-4 t} \ 3 e^{-t} & 0 & 0\end{array}\right] $ C

Question

Consider the first-order homogeneous system of linear differential equations

What is the general solution of this system? Here,  is an arbitrary constant vector.
A) $ \mathbf{x}(t)=\left(\begin{array}{lll}e^{t} & e^{4 t} & \left(t-\frac{1}{6}\right) e^{4 t} \ 6 e^{t} & -3 e^{4 t} & -3 t e^{4 t} \ 3 e^{t} & 0 & 0\end{array}\right) \mathbf{C} $ 
B) $ \mathbf{x}(t)=\left(\begin{array}{lll}e^{t} & e^{4 t} & \left(t+\frac{1}{6}\right) e^{4 t} \ 6 e^{t} & 3 e^{4 t} & 3 t e^{4 t} \ 3 e^{t} & 0 & 0\end{array}\right) $ C 
C) $ \mathbf{x}(t)=\left[\begin{array}{lll}e^{t} & e^{4 t} & \left(t+\frac{1}{6}\right) e^{4 t} \ -3 e^{t} & -3 e^{4 t} & 3 t e^{4 t} \ 6 e^{t} & 0 & 0\end{array}\right] $ C 
D) $ \mathbf{x}(t)=\left[\begin{array}{lll}e^{-t} & e^{-4 t} & \left(t+\frac{1}{6}\right) e^{-4 t} \ 6 e^{-t} & 3 e^{-4 t} & 3 t e^{-4 t} \ 3 e^{-t} & 0 & 0\end{array}\right] $ C

Quizplus · Accepted Answer

The Answer of Consider the first-order homogeneous system of linear differential equations

What is the general solution of this system? Here,  is an arbitrary constant vector.
A) $ \mathbf{x}(t)=\left(\begin{array}{lll}e^{t} & e^{4 t} & \left(t-\frac{1}{6}\right) e^{4 t} \ 6 e^{t} & -3 e^{4 t} & -3 t e^{4 t} \ 3 e^{t} & 0 & 0\end{array}\right) \mathbf{C} $ 
B) $ \mathbf{x}(t)=\left(\begin{array}{lll}e^{t} & e^{4 t} & \left(t+\frac{1}{6}\right) e^{4 t} \ 6 e^{t} & 3 e^{4 t} & 3 t e^{4 t} \ 3 e^{t} & 0 & 0\end{array}\right) $ C 
C) $ \mathbf{x}(t)=\left[\begin{array}{lll}e^{t} & e^{4 t} & \left(t+\frac{1}{6}\right) e^{4 t} \ -3 e^{t} & -3 e^{4 t} & 3 t e^{4 t} \ 6 e^{t} & 0 & 0\end{array}\right] $ C 
D) $ \mathbf{x}(t)=\left[\begin{array}{lll}e^{-t} & e^{-4 t} & \left(t+\frac{1}{6}\right) e^{-4 t} \ 6 e^{-t} & 3 e^{-4 t} & 3 t e^{-4 t} \ 3 e^{-t} & 0 & 0\end{array}\right] $ C

Consider the First-Order Homogeneous System of Linear Differential Equations