Unformatted text preview: u n ’s that satisﬁes u ( x, 1) = sin(2 πx )sin(3 πx ). (c) Show that for n = 1 , 2 , . . . , e u n ( x, y ) = sin( nπx ) sinh( nπ (1y )) satisﬁes u xx + u yy = 0 , u (0 , y ) = u (1 , y ) = u ( x, 1) = 0 . (d) Find a linear combination of the e u n ’s that satisﬁes u ( x, 0) = 2 sin( πx ). (e) Let D = (0 , 1) × (0 , 1). Solve the problem u xx + u yy = 0 in D, u (0 , y ) = u (1 , y ) = 0 , (0 ≤ y ≤ 1) , u ( x, 0) = 2 sin( πx ) , u ( x, 1) = sin(2 πx )sin(3 πx ) , (0 ≤ x ≤ 1) . 1...
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 Fall '08
 FriedmannBrock
 Math, Differential Equations, Equations, Partial Differential Equations, Linear combination, linear PDE Lu

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