Mathematics · Differential Equations

The two-point boundary value problem: y''(x) + λy(x) = 0 for x ∈ (0, π) y(0) = 0, y(π) = 0 has a trivial solution y = 0. It also has a non-trivial solution for:

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

λ = n 2 for all n &in; &naturals;

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The two-point boundary value problem: y''(x) + &lambda;y(x) = 0 for x &isin; (0, &pi;) y(0) = 0, y(&pi;) = 0 has a trivial solution y = 0. It also has a non-trivial solution for: