In the Previous Problem, Separate Variables Using $u ( r , \theta ) = R ( r ) \Theta ( \theta )$

Multiple Choice

In the previous problem, separate variables using $u ( r , \theta ) = R ( r ) \Theta ( \theta )$ . The resulting problems are

A) $r ^ { 2 } R ^ { \prime \prime } + r R ^ { \prime } - \lambda R = 0 , \Theta ^ { \prime \prime } - \lambda \Theta = 0 , \Theta ( \theta ) = \Theta ( \theta + 2 \pi )$
B) $r ^ { 2 } R ^ { \prime \prime } + r R ^ { \prime } + \lambda R = 0 , \Theta ^ { \prime \prime } + \lambda \Theta = 0 , \Theta ( \theta ) = \Theta ( \theta + 2 \pi )$
C) $r ^ { 2 } R ^ { \prime \prime } + r R ^ { \prime } - \lambda R = 0 , \Theta ^ { \prime \prime } + \lambda \Theta = 0 , \Theta ( \theta ) = \Theta ( \theta + 2 \pi )$
D) $r ^ { 2 } R ^ { \prime \prime } + r R ^ { \prime } - \lambda R = 0 , \Theta ^ { \prime \prime } + \lambda \Theta = 0 , \Theta ( \theta ) = \Theta ( \theta + \pi )$
E) $r ^ { 2 } R ^ { \prime \prime } + r R ^ { \prime } + \lambda R = 0 , \Theta ^ { \prime \prime } + \lambda \Theta = 0 , \Theta ( \theta ) = \Theta ( \theta + \pi )$