In the Problem , the Eigenvalues and Eigenfunctions of the Underlying Homogeneous Problem

question 26

Multiple Choice

In the problem $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + x e ^ { t } = \frac { \partial u } { \partial t } , u ( 0 , t ) = 0 , u ( L , t ) = 0 , u ( x , 0 ) = 0$ , the eigenvalues and eigenfunctions of the underlying homogeneous problem are

• A) \(\lambda = n ^ { 2 } , X = \sin ( n x )\)
• B) \(\lambda = n ^ { 2 } , X = \cos ( n x )\)
• C) \(\lambda = n ^ { 2 } \pi ^ { 2 } / L ^ { 2 } , X = \sin ( n \pi x / L )\)
• D) \(\lambda = n ^ { 2 } \pi ^ { 2 } / L ^ { 2 } , X = \cos ( n \pi x / L )\)
• E) \(\lambda = n ^ { 2 } \pi ^ { 2 } , X = \sin ( n \pi x )\)

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