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

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

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