Solution: The problems for Section 3.8 deal with eigenvalues and eigenfunctions and may
Chapter , Problem 5(choose chapter or problem)
The problems for Section 3.8 deal with eigenvalues and eigenfunctions and may be used here as well. In 1 through 5, verify that the eigenvalues and eigenfunctions for the indicated SturmLiouville problem are those listed.y00 C y D 0, hy.0/ y0.0/ D hy.L/ C y0.L/ D 0 (h>0);n D 2n=L2, yn.x/ D n cos nx=L C hL sin nx=L (n =1), where n is the nth positive root of tan x D 2hLx=.x2h2L2/. Estimate n for n large by sketching the graphs ofy D 2hL cot x and the hyperbola y D .x2 h2L2/=x.6
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