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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 = A φ (0) = φ (2 π ) B = 2 π A + B A = 0 φ (0) = φ (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) = φ (2 π ) λA λB = λAe λ 2 π λ Be 2 π λ A [1 e 2 π λ ] + B [1 e 2 π λ ] = 0 λ A 1 e 2 π λ B λ 1 e 2 π λ = 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 e 2 π
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