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Unformatted text preview: of separation of variables to nd all solutions of the form u ( x, y ) = F ( x ) G ( y ). a . u x-u y = 0 b . u x + u y = ( x + y ) u c . u xy-u = 0 d . xu xy + 2 yu = 0 e . Show that it is impossible to write the function u ( x, y ) = x + y as u ( x, y ) = F ( x ) G ( y ), a product of two dierentiable functions. (Hint: If it were possible, show how a simple calculation would yield an impossible conclusion.) 1...
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- Summer '08