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Unformatted text preview: b) Put this equation in self-adjoint form. c) Identify the eigenvalue. d) Identify the weight function. 3) One solution of Laguerre’s di±erential equation xy ′′ + (1-x ) y ′ + ny = 0 for n = 0 is y 1 ( x ) = 1. Develop a second, linearly independent solution. 4) Construct the Green’s function for the operator d 2 /dx 2 and the boundary conditions y (0) = 0 and y ′ (1) = 0. Consider now the equation y ′′ ) x ) + λy ( x ) = 0 with the same boundary conditions. Obtain the solutions. Verify that the solutions satisfy y ( x ) = λ I 1 G ( x, t ) y ( t ) dt Good Luck...
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- Spring '10