The Solution of the Eigenvalue Problem $y ^ { \prime \prime } + \lambda y = 0 , y ^ { \prime } ( 0 ) = 0 , y ^ { \prime } ( \pi ) = 0$

question 11

Multiple Choice

The solution of the eigenvalue problem $y ^ { \prime \prime } + \lambda y = 0 , y ^ { \prime } ( 0 ) = 0 , y ^ { \prime } ( \pi ) = 0$ is

• A) \(\lambda = n , y = \cos ( n x ) , n = 0,1,2 , \ldots\)
• B) \(\lambda = n , y = \sin ( n x ) , n = 1,2,3 , \ldots\)
• C) \(\lambda = n ^ { 2 } , y = \cos ( n x ) , n = 0,1,2 , \ldots\)
• D) \(\lambda = n ^ { 2 } , y = \sin ( n x ) , n = 1,2,3 , \ldots\)
• E) \(\lambda = n , y = \cos ( n x ) + \sin ( n x ) , n = 1,2,3 , \ldots\)

---

Definitions:

Perceptual Set

A psychological framework that predisposes individuals to perceive information in a particular way based on their expectations, emotions, and experiences.

Influenced

The capacity to have an effect on the character, development, or behavior of someone or something.

Perception

The method through which people structure and understand their sensory experiences to assign significance to the world around them.

Opponent Process Theory

Opponent process theory is a psychological and neurological model that explains how the perception of one stimulus (color or emotion) can be affected by the aftereffects of another stimulus.