The Solution Of $y ^ { \prime \prime } - n ^ { 2 } y = 0 , y ( 0 ) = 0 , y ( \pi ) = 0 , n = 1,2,3 \ldots$

question 6

Multiple Choice

The solution of $y ^ { \prime \prime } - n ^ { 2 } y = 0 , y ( 0 ) = 0 , y ( \pi ) = 0 , n = 1,2,3 \ldots$ is

• A) \(y = 0\)
• B) \(y = c \cdot \sin ( n x )\)
• C) \(y = c \cdot \cos ( n x )\)
• D) \(y = c \left( e ^ { n x } - e ^ { - n x } \right)\)
• E) \(y = c \left( e ^ { n x } + e ^ { - n x } \right)\)

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Definitions:

Irresistible Impulse Rule

A legal defense asserting that a defendant was unable to control their actions due to a mental illness, making them not responsible for the criminal behavior.

M'Naghten Rule

A standard for defining legal insanity, which asserts that a defendant must be found mentally incapable of understanding the nature of his actions or distinguishing right from wrong at the time of the offense.

Hallucinations

Perceptions in any sensory modality without an external stimulus, creating experiences that seem real but are not.

Schizophrenia

A mental disorder characterized by disturbances in thought, perception, and behavior, leading to a disconnection from reality.