Find the eigenvalues i, and eigenfunctions y,(x) for the given boundary-value problem. (Give your ans y" + Ày = 0, y(0) = 0, y'(T/2) = 0 2, = (2n – 1)2 n = 1, 2, 3, ... Y,(x) = sin (2n – 1)x ,n = 1, 2, 3, ...

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A: dydtdxdt=5x-yx-885y-xy-88dydx=-x-8y-8∫y-8dy=∫8-xdxy22-8y=8x-x22+cy2-16y=16x-x2+Cx2+y2-16x+y=C

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Q: 3. (a) Find the eigenvalues and eigenfunctions of the boundary-value problem x2y'' + xy' + (lamda)y…

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Q: 1. Show that the eigenvalues and eigenfunctions of the Sturm-Liouville problem y" + Xy = 0, y(0) +…

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Q: Use eigenfunction expantion methodto solve: d y 1 -(xy')- dx y(1) = e, y(e) =0 : %3D

A: Given, ddxxy'-yx=1xxy''+y'-yx=1xx2y''+xy-y=1....1 Let, x=et then, x2y''=θθ-1yWhere, θ=ddt then,xy'=θ…

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Q: 7. Show that the integral equation R has no eigenvalues. g(x) = a √ (sin x sin 2t) g(t) dt

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