MATH 115 Midterm: MATH 115 UPenn 115Fall 05Post
Document Summary
Write the following ode in a sturm-liouville problem in self-adjoint form, and write down the orthog- onal relation between any two eigenfunctions y1(x), y2(x) in terms of an integral. y . + y = 0 y(0) = 0, y(4) = 0. The integral factor is er sin xdx = e cos x, multiply this to the equation and get e cos xy . E cos xy = 0, in the self-adjoint form as. Therefore the eigenfunctions are orthogonal with respect to the weight function e cos x, and explicitly, for any two eigenfunctions y1(x), y2(x), we have.
