In the Previous Four Problems, the Infinite Series Solution Is $u = \sum _ { n - 1 } ^ { \infty } c _ { n } J _ { 0 } ( n \pi r / 3 ) \cos ( n \pi z / 3 )$

In the previous four problems, the infinite series solution is (for certain values of the constants)

A) $u = \sum _ { n - 1 } ^ { \infty } c _ { n } J _ { 0 } ( n \pi r / 3 ) \cos ( n \pi z / 3 )$
B) $u = \sum _ { n - 1 } ^ { \infty } c _ { n } J _ { 0 } \left( n ^ { 2 } \pi ^ { 2 } r / 9 \right) \cos ( n \pi z / 3 )$
C) $u = \sum _ { n - 1 } ^ { \infty } c _ { n } J _ { 0 } \left( n ^ { 2 } \pi ^ { 2 } r / 9 \right) \sin ( n \pi z / 3 )$
D) $u = \sum _ { n - 1 } ^ { \infty } c _ { n } J _ { 0 } \left( z _ { n } r / 2 \right) \sinh \left( z _ { n } ( z - 3 ) / 2 \right)$
E) $u = \sum _ { n = 1 } ^ { \infty } c _ { n } J _ { 0 } \left( z _ { n } r \right) \cosh \left( z _ { n } ( z - 3 ) \right)$