18.(0) Find the eigenvalues and the normalized.eigenfunctions of the following bounidary value problem: x'y+xy'+Ay 0, (b)...

Transcribed Image Text:

18.(0) Find the eigenvalues and the normalized.eigenfunctions of the following bounidary value problem: x'y"+xy'+Ay 0, (b) Find the eigenfunction expansion of the solution of the following boundary value problems éinx <me 1<x<e' \,}(i) = 0, y(c*) = 0 (ifthey exist): (i) x*y" +xy+y=1, (i) x*y"+xy'+2y = 1, (ii) x'y" +xy'+4y = 1, „Y(1) = 0, y(e") =0 No »y(1) = 0, y(e") = 0 1<x<e* 1<x<e* 1<x<e* „y(1) = 0, y(e") = 0 18.(0) Find the eigenvalues and the normalized.eigenfunctions of the following bounidary value problem: x'y"+xy'+Ay 0, (b) Find the eigenfunction expansion of the solution of the following boundary value problems éinx <me 1<x<e' \,}(i) = 0, y(c*) = 0 (ifthey exist): (i) x*y" +xy+y=1, (i) x*y"+xy'+2y = 1, (ii) x'y" +xy'+4y = 1, „Y(1) = 0, y(e") =0 No »y(1) = 0, y(e") = 0 1<x<e* 1<x<e* 1<x<e* „y(1) = 0, y(e") = 0