Question: Find the eigenvalues and eigenfunctions. Verify orthogonality. Start by writing the ODE in the form (1), using Prob. 6. Show details of your work. (y'/x)'

Find the eigenvalues and eigenfunctions. Verify orthogonality. Start by writing the ODE in the form (1), using Prob. 6. Show details of your work.

(y'/x)' + (λ + 1)y/x3 = 0, y(1) = 0, y(eπ) = 0. (Set x = et.)

Data from Prob. 6

Show that y" + fy' + (g + λh) y = 0 takes the form (1) if you set p = exp (∫f dx), q = pg, r = hp. Why would you do such a transformation?

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