In the Previous Two Problems, the Solution For $u$ Takes the Form
A)

In the previous two problems, the solution for $u$ takes the form

A) $u ( x , t ) = \sum _ { n - 1 } ^ { \infty } u _ { n } ( t ) \sin ( n \pi x / L )$
B) $u ( x , t ) = \sum _ { n = 1 } ^ { \infty } u _ { n } ( t ) \cos ( n \pi x )$
C) $u ( x , t ) = \sum _ { n - 1 } ^ { \infty } u _ { n } ( t ) \sin \left( n ^ { 2 } \pi ^ { 2 } x ^ { 2 } / L ^ { 2 } \right)$
D) $u ( x , t ) = \sum _ { n - 1 } ^ { \infty } u _ { n } ( t ) \cos \left( n ^ { 2 } \pi ^ { 2 } x ^ { 2 } / L ^ { 2 } \right)$
E) $u ( x , t ) = \sum _ { n - 1 } ^ { \infty } u _ { n } ( t ) \sin ( n \pi x )$