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Differential Equations Lecture Work Solutions 173

Differential Equations Lecture Work Solutions 173 - 4a y y...

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4a. y + λy = 0 0 < x < π y (0) = 0 y ( π ) = 0 λ n = n + 1 2 2 cos( n + 1 2 ) x To get orthonormal set, we need to divide by the normalization factor, || y n || = π 0 cos 2 ( n + 1 2 ) xdx = π/ 2 The normalized eigenfunctions are cos( n + 1 2 ) x π/ 2 4b. y + (1 + λ ) y = 0 0 < x < π
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