The Solution of the System $\frac { d x } { d t } = - 6 x - 5 y , \frac { d y } { d t } = 3 x + 2 y$

question 17

Multiple Choice

The solution of the system $\frac { d x } { d t } = - 6 x - 5 y , \frac { d y } { d t } = 3 x + 2 y$ is

• A) \(x = 3 c _ { 1 } e ^ { - 3 t } + c _ { 2 } e ^ { - t } , y = - 5 c _ { 1 } e ^ { - 3 t } - c _ { 2 } e ^ { - t }\)
• B) \(x = 3 c _ { 1 } e ^ { 3 t } - c _ { 2 } e ^ { - t } , y = - 5 c _ { 1 } e ^ { 3 t } + c _ { 2 } e ^ { - t }\)
• C) \(x = 3 c _ { 1 } e ^ { 3 t } + c _ { 2 } e ^ { t } , y = - 5 c _ { 1 } e ^ { 3 t } - c _ { 2 } e ^ { t }\)
• D) \(x = 5 c _ { 1 } e ^ { 3 t } + c _ { 2 } e ^ { t } , y = - 3 c _ { 1 } e ^ { 3 t } - c _ { 2 } e ^ { t }\)
• E) \(x = 5 c _ { 1 } e ^ { - 3 t } + c _ { 2 } e ^ { - t } , y = - 3 c _ { 1 } e ^ { - 3 t } - c _ { 2 } e ^ { - t }\)

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Definitions:

Tehran Conference

A strategy meeting of Joseph Stalin, Franklin D. Roosevelt, and Winston Churchill from 28 November to 1 December 1943, during World War II, held in Tehran, Iran, which focused on war strategy and post-war reorganization.

Yalta Conference

Meeting of Franklin D. Roosevelt, Winston Churchill, and Joseph Stalin at a Crimean resort to discuss the postwar world on February 4–11, 1945; Joseph Stalin claimed large areas in eastern Europe for Soviet domination.

Iron Curtain

Term coined by Winston Churchill to describe the Cold War divide between western Europe and the Soviet Union’s eastern European satellites.

Capitalist West

Refers to Western countries, primarily in Europe and North America, that operate under a capitalist economic system, emphasizing private ownership and the free market.