In the Previous Four Problems, the Infinite Series Solution of the Original

question 4

Multiple Choice

In the previous four problems, the infinite series solution of the original problem is (for certain values of the constants $a _ { n }$ and $b _ { n }$ )

• A) \(u = \sum _ { n = 1 } ^ { \infty } a _ { n } J _ { 0 } \left( z _ { n } r / 2 \right) \cos \left( z _ { n } t / 2 \right)\)
• B) \(u = \sum _ { n = 1 } ^ { \infty } b _ { n } J _ { 0 } \left( z _ { n } r / 2 \right) \sin \left( z _ { n } t / 2 \right)\)
• C) \(u = \sum _ { n = 1 } ^ { \infty } b _ { n } J _ { 0 } ( n \pi r ) \sin ( n \pi t )\)
• D) \(u = \sum _ { n = 1 } ^ { \infty } a _ { n } J _ { 0 } ( n \pi r ) \cos ( n \pi t )\)
• E) \(u = \sum _ { n - 1 } ^ { \infty } J _ { 0 } \left( z _ { n } r / 2 \right) \left( a _ { n } \cos ( n \pi t ) + b _ { n } \sin ( n \pi t ) \right)\)