The Solution of the System of Differential Equations $\begin{array} { l } \frac { d x } { d t } = x + 2 y \\\frac { d y } { d t } = 4 x + 3 y\end{array}$

question 25

Multiple Choice

The solution of the system of differential equations $\begin{array} { l } \frac { d x } { d t } = x + 2 y \\\frac { d y } { d t } = 4 x + 3 y\end{array}$ is

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

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Definitions:

Vijayanagara's Sacred Center

The spiritual core of the Vijayanagara Empire, featuring temple complexes and religious monuments.

Garbha Griha

Hindi, “womb chamber.” In Hindu temples, the cella, the holy inner sanctum often housing the god’s image or symbol.

Stupa

A dome-shaped structure erected as a Buddhist shrine in South Asia, serving as a marker for sacred relics or commemorating significant events in Buddhism.

Punjab Hills

A region in north India known for its distinct art styles, particularly in miniatures and paintings, which often depict themes from Hindu mythology and nature.