Differential Equations Lecture Work Solutions 56

Differential Equations Lecture Work Solutions 56 - = n2...

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Since λ should be positive λ = n 2 n =1 , 2 , ... λ n = n 2 φ n = A n cos nx + B n sin nx λ =0 φ = Ax + B φ 0 = A φ (0) = φ (2 π ) B =2 πA + B A =0 φ 0 (0) = φ 0 (2 π ) A = A λ =0 φ = B λ< 0 φ = Ae λx + Be λx φ (0) = φ (2 π ) A + B = Ae λ 2 π + Be 2 π λ φ 0 (0) = φ 0 (2 π ) λA λB = λAe λ 2 π λBe 2 π λ A [1 e 2 π λ ]+ B [1 e 2 π λ ]=0 λA h 1 e 2 π λ i B λ h 1 e 2 π λ i =0 1 e 2 π λ 1 e 2 π λ λ (1 e 2 π λ ) λ (1 e 2 π λ ) =0 λ (1
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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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