Question: 1) Explain how to find all eigenvalues > and eigenfunctions y( ) solutions of the eigenfunction problem -y = >y, y'(0) = 0, y(5) =

1) Explain how to find all eigenvalues > and eigenfunctions y( ) solutions of the eigenfunction problem -y" = >y, y'(0) = 0, y(5) = 0. Label the eigenfunctions with an index 7 - 1, 2, 3, . . .. Show all the steps needed to find the eigenvalues and eigenfunctions. 2) Show, with an explicit calculation, that the eigenfunction with 7 = 1 is orthogonal to the eigenfunction with n = 2. Hint: The following trigonometric identities may or may not be useful, sin(c) sin (B) = 2 (cos(a - B) - cos(a + B) ), cos(a ) Cos (B) - (cos(a - B) + cos(a + B))

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