Find all real eigenvalue and eigenfunctions to the following:
(xy')' + rx^(-1)y = 0
y'(0)=0 ; y(e^pi)=0
This is problem #19 to Fundamentals of Differential Equations and Boundary Value Problems 6th Edition.

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x2y"+xy'+ry=0
a2+r=0
r should be w2
so a=+-j(or i)
y_1=coshlnwx
y_2=sinhlnwx

and fix your question y"(0)=0 change to y'(1)=0 !

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