{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Differential Equations Lecture Work Solutions 55

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
3. φ + λ φ = 0 φ (0) = φ (2 π ) φ (0) = φ (2 π ) λ > 0 φ = A cos λ x + B sin λ x φ = A λ sin λx + B λ cos λ x φ (0) = φ (2 π ) A = A cos 2 π λ + B sin 2 π λ φ (0) = φ (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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}