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

question 18

Multiple Choice

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) \(x = \left( e ^ { - t } - 5 t e ^ { - t } \right) / 3 , y = - 5 t e ^ { - t } / 3\)

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