Consider the following ODE with boundary conditions y" + xy = 0, y(0) = 0, y 3πT = 0. Which of the following values of A belong to the eigenvalues of the problem? (A); ²; 25²; (B) -;-1; -25; (C) 1; 9; 25; (D) 25; 4; 4;

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A: Here we have to verify that λi  is an eigenvalue of A and that xi is a corresponding eigenvector .

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A: We can calculate eigenvalues By |A-λI|=0

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A: To find the eigenvectors η, solve A-λ Iη=0 for each eigenvalue λ