Differential Equations Lecture Work Solutions 59

Differential Equations Lecture Work Solutions 59 - 5. uxx +...

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5. u xx + u yy =0 u x (0 ,y )=0 u x ( L, y )=0 u ( x, 0) = 0 u ( x, H )= f ( x ) u ( x, y )= X ( x ) Y ( y )= X 0 X = Y 0 Y = λ u x (0 ,y )=0 X 0 (0) = 0 u x ( L, y )=0 X 0 ( L )=0 u ( x, 0) = 0 Y (0) = 0 X 0 + λX =0 Y 0 λY =0 X 0 (0) = 0 Y (0) = 0 X 0 ( L )=0 Table at the end of Chapter 4 λ n = L ± 2 n =0 , 1 , 2 , ... x n =co s L x Y 0 n L ± 2 Y n =0 n =0 , 1 , 2 , ... If n =0 Y 0 0 =0 Y 0 = A 0 y + B 0 Y 0 (0) = 0 B 0 =0 Y 0 ( y )=
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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