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Consider the singular Sturm-Liouville eigenvalue problem (d/dx (x du/dx))+ lambda* x^(-1) u=0 0 < x < 1; u(1) = 0:

Consider the singular Sturm-Liouville eigenvalue problem

(d/dx (x du/dx))+ lambda* x^(-1) u=0
0 < x < 1;
u(1) = 0:
a) Specify an appropriate boundary condition at x = 0 to ensure that the problem is self-adjoint.
b) Use the Rayleigh quotient to show that there are no negative eigenvalues.
c) Find two linearly independent solutions to the di erential equation.
d) Find the spectrum and eigenfunctions.Consider the singular Sturm-Liouville eigenvalue problem

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