In the Problem , the Eigenvalues and Eigenfunctions of the Underlying Homogeneous Problem

question 26

Multiple Choice

In the problem $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + x e ^ { t } = \frac { \partial u } { \partial t } , u ( 0 , t ) = 0 , u ( L , t ) = 0 , u ( x , 0 ) = 0$ , the eigenvalues and eigenfunctions of the underlying homogeneous problem are

• A) \(\lambda = n ^ { 2 } , X = \sin ( n x )\)
• B) \(\lambda = n ^ { 2 } , X = \cos ( n x )\)
• C) \(\lambda = n ^ { 2 } \pi ^ { 2 } / L ^ { 2 } , X = \sin ( n \pi x / L )\)
• D) \(\lambda = n ^ { 2 } \pi ^ { 2 } / L ^ { 2 } , X = \cos ( n \pi x / L )\)
• E) \(\lambda = n ^ { 2 } \pi ^ { 2 } , X = \sin ( n \pi x )\)

---

Definitions:

Low Carbohydrate Diet

A dietary strategy that limits carbohydrate intake, focusing on protein, fat, and low-carb vegetables instead.

Craves

Strongly desires or yearns for something or someone.

Ironic Processing

The psychological process where attempts to suppress certain thoughts make them more likely to surface.

Thought Suppression

The process of consciously attempting to avoid thinking certain thoughts.