Consider the Equation $u _ { xx } - u _ { t } = 0$

question 18

Multiple Choice

Consider the equation $u _ { xx } - u _ { t } = 0$ with conditions $u ( 0 , t ) = 0 , u _ { x } = ( L , t ) = 0 , u ( x , 0 ) = f ( x )$ . When separating variables with $u ( x , t ) = X ( x ) T ( t )$ , the resulting problems for $X , T$ are

• A) \(X ^ { \prime \prime } + \lambda X = 0 , X ( 0 ) = 0 , X ^ { \prime } ( L ) = 0 , T ^ { \prime } - \lambda T = 0 , T ( 0 ) = f ( x )\)
• B) \(X ^ { \prime \prime } + \lambda X = 0 , X ( 0 ) = 0 , X ^ { \prime } ( L ) = 0 , T ^ { \prime } + \lambda T = 0 , T ( 0 ) = f ( x )\)
• C) \(X ^ { \prime \prime } - \lambda X = 0 , X ( 0 ) = 0 , X ^ { \prime } ( L ) = 0 , T ^ { \prime } + \lambda T = 0\)
• D) \(X ^ { \prime \prime } + \lambda X = 0 , X ( 0 ) = 0 , X ^ { \prime } ( L ) = 0 , T ^ { \prime } - \lambda T = 0\)
• E) \(X ^ { \prime \prime } + \lambda X = 0 , X ( 0 ) = 0 , X ^ { \prime } ( L ) = 0 , T ^ { \prime } + \lambda T = 0\)

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