Find eigenvalues of the sturm-liouville problem

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Reference no: EM131548052

Question 1:

1. Find all the eigenvalues and eigenfunctions of the Sturm-Liouville problem.

2. Use the integral inner product to verify the orthogonality of the eigenfunctions.

y" + λy = 0, y (0) = 0, y (3) = 0

Question 2:

1. Find all the eigenvalues and eigenfunctions of the Sturm-Liouville problem.

2. Use the integral inner product to verify the orthogonality of the eigenfunctions.

y" + λy = 0, y'(0) = 0, y'(Π/2) = 0

Question 3:

1. Find all the eigenvalues and eigenfunctions of the Sturm-Liouville problem.

2. Use the integral inner product to verify the orthogonality of the eigenfunctions.

y'' + λy = 0, y (0) =0, y' (4) =0

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The solution to the heat equation is given by the last equation after using separation of variables technique. The solution is a product of sine and exponential functions and satisfies the boundary and initial conditions that were given.

Reference no: EM131548052

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