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

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

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

Correct Answer:

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