a) Let T(x), n = 1,2,3, ... are the eigenfunctions of the Sturm-Liouville problem; x³y" + 2x²y' + λy = 0, y(1) = 5, y'(3) = 6. Set up the orthogonality condition. b) Write the Fourier-Legendre expansion of the function f(x) = 2x3 - 1.

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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a) Let T(x), n = 1,2,3, ... are the eigenfunctions of the Sturm-Liouville
problem; x³y" + 2x²y' + λy = 0, y(1) = 5, y'(3) = 6.
Set up the orthogonality condition.
b) Write the Fourier-Legendre expansion of the function f(x) = 2x3 - 1.
Transcribed Image Text:a) Let T(x), n = 1,2,3, ... are the eigenfunctions of the Sturm-Liouville problem; x³y" + 2x²y' + λy = 0, y(1) = 5, y'(3) = 6. Set up the orthogonality condition. b) Write the Fourier-Legendre expansion of the function f(x) = 2x3 - 1.
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