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

question 24

Multiple Choice

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

• A) \(x = \left( c _ { 1 } + c _ { 2 } / 5 \right) e ^ { - t } + c _ { 2 } t e ^ { - t } - 4 t + 69 / 5 , y = c _ { 1 } e ^ { - t } + c _ { 2 } t e ^ { - t } - 5 t - 16\)
• B) \(x = \left( c _ { 1 } + c _ { 2 } / 5 \right) e ^ { - t } + c _ { 2 } t e ^ { - t } + 4 t + 69 / 5 , y = c _ { 1 } e ^ { - t } + c _ { 2 } t e ^ { - t } - 5 t + 16\)
• C) \(x = \left( c _ { 1 } + c _ { 2 } / 5 \right) e ^ { t } + c _ { 2 } t e ^ { t } - 4 t + 69 / 5 , y = c _ { 1 } e ^ { t } + c _ { 2 } t e ^ { t } - 5 t + 16\)
• D) \(x = \left( c _ { 1 } - c _ { 2 } / 5 \right) e ^ { - t } + c _ { 2 } t e ^ { - t } - 4 t + 69 / 5 , y = c _ { 1 } e ^ { - t } + c _ { 2 } t e ^ { - t } - 5 t + 16\)
• E) \(x = \left( c _ { 1 } + c _ { 2 } / 5 \right) e ^ { - t } + c _ { 2 } t e ^ { - t } - 4 t + 69 / 5 , y = c _ { 1 } e ^ { - t } + c _ { 2 } t e ^ { - t } - 5 t + 16\)

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Definitions:

Brachioradialis

A muscle of the forearm that flexes the forearm at the elbow, especially when the forearm is in a midposition between pronation and supination.

Biceps Brachii

A muscle of the upper arm that flexes the elbow and rotates the forearm, consisting of two heads that join on the radius.

Triceps Brachii

A muscle of the back of the upper arm responsible for extension of the elbow.

Anconeus

A small muscle located at the elbow, involved in extending the elbow and stabilizing the elbow joint.