Solve the Initial Value Problem $$\frac { \mathrm { d } ^ { 2 } y } { d x ^ { 2 } } = - 5 e ^ { - x } , y ( 0 ) = - 4 , y ^ { \prime } ( 0 ) = 0$$

question 131

Multiple Choice

Solve the initial value problem.
- $$\frac { \mathrm { d } ^ { 2 } y } { d x ^ { 2 } } = - 5 e ^ { - x } , y ( 0 ) = - 4 , y ^ { \prime } ( 0 ) = 0$$

• A) \(y = - 5 e ^ { - x } - 4\)
• B) \(y = - 5 e ^ { - x } + 5 x - 9\)
• C) \(y = 5 e ^ { - x } + C\)
• D) \(y = - 5 e ^ { - x } - 5 x + 1\)

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Definitions:

Reflex Arc

A neural pathway that mediates an automatic response to a stimulus, involving sensory input and motor output without conscious thought.

Dualistic Nature

The concept of two fundamental parts or principles, such as mind and body, in contrast or opposition.

Descartes

René Descartes, a 17th-century French philosopher, mathematician, and scientist, known for his statement "I think, therefore I am" and his contributions to modern philosophy and the development of the Cartesian coordinate system.

Instinct

Instinct denotes the inherent inclination of a living organism towards a particular complex behavior, which is unlearned and often serves survival and reproductive purposes.