The Solution of the System of Differential Equations $\begin{array} { l } \frac { d x } { d t } = - 6 x + 5 y \\\frac { d y } { d t } = - 5 x + 4 y \\x ( 0 ) = 1 / 3 , y ( 0 ) = 0\end{array}$

The solution of the system of differential equations $\begin{array} { l } \frac { d x } { d t } = - 6 x + 5 y \\\frac { d y } { d t } = - 5 x + 4 y \\x ( 0 ) = 1 / 3 , y ( 0 ) = 0\end{array}$ is

A) $x = \left( e ^ { t } - 5 t e ^ { t } \right) / 3 , y = - 5 t e ^ { t } / 3$
B) $x = \left( e ^ { - t } - t e ^ { - t } \right) / 3 , y = - t e ^ { - t } / 3$
C) $x = \left( e ^ { - t } + t e ^ { - t } \right) / 3 , y = t e ^ { - t } / 3$
D) $x = \left( e ^ { - t } + 5 t e ^ { - t } \right) / 3 , y = 5 t e ^ { - t } / 3$
E) $x = \left( e ^ { - t } - 5 t e ^ { - t } \right) / 3 , y = - 5 t e ^ { - t } / 3$

Correct Answer:

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