Differential Equations Lecture Work Solutions 89

Differential Equations Lecture Work Solutions 89 - 19. 2 u...

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19. 2 u =0 , 0 x π, 0 y π u ( x, 0) = π 2 x 2 +2 πx 3 x 4 u ( x, π )=0 u (0 ,y )= u ( π, y )=0 The only diference is in the inhomogeneous condition, thus the general solution is the same u ( x, y )= X n =1 a n sinh n ( y π )sin nx Now use the only inhomogeneous boundary condition π 2 x 2 +2 πx 3 x 4 = u ( x, 0) = X n =1 a n sinh sin nx The coefficients a n sinh are those oF the ±ourier sine expansion oF π 2 x 2 +2 πx 3 x 4 , i.e. a n sinh = 2 π Z π 0 π 2 x 2 +2 πx 3 x 4 sin nxdx Now we integrate (using integration by parts to reduce the powers oF
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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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