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Math 286 Conflict Midterm 3 Solutions(1) LetLbe a positive constant.Find the (non-negative) eigenvaluesand associated eigenfunctions of(y00+λy= 0y(0) = 0,y0(L) = 0
(2) LetAbe ann×nmatrix and letλbe an eigenvalue ofAwithassociated eigenvectorvRn.a) Letωbe a (possibly complex) number such thatω2=λ.Showthat the functionx(t) =eωtvsatisfiesx00(t) =Ax.b) Using the method of part (a), find four distinct solutions to thesecond order systemx00=4114x.Solution.

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