Differential Equations Lecture Work Solutions 55

Differential Equations Lecture Work Solutions 55 - 3. + = 0...

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3. φ 0 + λφ =0 φ (0) = φ (2 π ) φ 0 (0) = φ 0 (2 π ) λ> 0 φ = A cos λx + B sin λx φ 0 = A λ sin λx + B λ cos λx φ (0) = φ (2 π ) A = A cos 2 π λ + B sin 2 π λ φ 0 (0) = φ 0 (2 π ) B λ = A λ sin 2 π λ + B λ cos 2 π λ A (1 cos 2 π λ ) B sin 2 π λ =0 A λ sin 2 π λ + B λ (1 cos 2 π λ )=0 A system of 2 homogeneous equations. To get a nontrivial solution one must have the determinant = 0. 1 cos 2 π λ sin 2 π λ λ sin 2 π λ λ (1 cos 2 π
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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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