The Solutions of the Eigenvalue Problem and the Other Problem $\lambda = n \pi , X = \cos ( n \pi x ) , Y = \sinh ( n \pi y ) , n = 1,2,3 , \ldots$

Multiple Choice

The solutions of the eigenvalue problem and the other problem from the previous problem are

A) $\lambda = n \pi , X = \cos ( n \pi x ) , Y = \sinh ( n \pi y ) , n = 1,2,3 , \ldots$
B) $\lambda = n \pi , X = \sin ( n \pi x ) , Y = \sinh ( n \pi y ) , n = 1,2,3 , \ldots$
C) $\lambda = n ^ { 2 } \pi ^ { 2 } , X = \cos ( n \pi x ) , Y = \sinh ( n \pi y ) , n = 1,2,3 , \ldots$
D) $\lambda = n ^ { 2 } \pi ^ { 2 } , X = \sin ( n \pi x ) , Y = \sinh ( n \pi y ) , n = 1,2,3 , \ldots$
E) $\lambda = n ^ { 2 } \pi ^ { 2 } , X = \cos ( n \pi x ) , Y = \sinh ( n \pi y ) , n = 0,1,2 , \ldots , ( Y = y \text { if } n = 0 )$