4038HW20_Su2010

4038HW20_Su2010 - of separation of variables to nd all...

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Homework #20 Math 4038 Summer 2010 Print Your Name: S how all work: We can give credit only for what you write! Hand in only your own work—nothing copied! Please do not convert exact answers into decimal approximations. Please write neatly so that the grader can read your work easily. You may print a copy of this Fle and write on it, or use a blank paper with your name at the top. The maximum score possible is 10. Questions, of which Part (b) only is to be handed in. For parts (a)–(d), use the method
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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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