The Solution Of $r ^ { 2 } R ^ { \prime \prime } + r R ^ { \prime } + \lambda R = 0 , R ( 1 ) = 0 , R ( 2 ) = 0$

Multiple Choice

The solution of $r ^ { 2 } R ^ { \prime \prime } + r R ^ { \prime } + \lambda R = 0 , R ( 1 ) = 0 , R ( 2 ) = 0$ is

A) $\lambda = n \pi / \ln 2 , R = \sin ( n \pi \ln r / \ln 2 )$
B) $\lambda = ( n \pi / \ln 2 ) ^ { 2 } , R = \sin ( n \pi \ln r / \ln 2 )$
C) $\lambda = ( n \pi / \ln 2 ) ^ { 2 } , R = \cos ( n \pi \ln r / \ln 2 )$
D) $\lambda = n \pi / \ln 2 , R = \cos ( n \pi \ln r / \ln 2 )$
E) none of the above