In the Previous Problem, the Eigenfunction Expansion If $x e ^ { t }$

Multiple Choice

In the previous problem, the eigenfunction expansion if $x e ^ { t }$ is

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