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

question 19

Multiple Choice

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

• A) \(y = \sin ( n x ) , \lambda = n ^ { 2 } , n = 1,2,3 , \ldots\)
• B) \(y = \cos ( n x ) , \lambda = n ^ { 2 } , n = 1,2,3 , \ldots\)
• C) \(y = \sin ( n x ) , \lambda = n , n = 1,2,3 , \ldots\)
• D) \(y = \cos ( n x ) , \lambda = n , n = 1,2,3 , \ldots\)
• E) none of the above

---

Definitions:

Perceptual Constancy

The brain's ability to recognize that objects are unchanging (in shape, size, brightness, or color) despite shifts in environment or perspective.

Illumination

The provision of light, enabling visibility in an environment, or the state of being lit with light.

Blindsight

A phenomenon in which individuals with damage to their primary visual cortex are capable of responding to visual stimuli that they do not consciously see.

Retinal Image

The projection of visual stimuli on the retina, the light-sensitive layer at the back of the eye, forming the basis for visual perception.