When $u ( x , y ) = X ( x ) Y ( y )$

question 8

Multiple Choice

When $u ( x , y ) = X ( x ) Y ( y )$ is substituted into the equation $u _ { xx } + u _ { y y } = 0$ , the resulting equations for $X$ and $Y$ are

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

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