The Hermite differential equation is given by y" – 2xy' + ày = 0. Rewrite this equation in self-adjoint form. From the Sturm-Liouville form obtained, verify that the differential operator is self-adjoint on (-0, 00). Give the integral form for the orthogonality of the eigenfunctions.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**5.** The Hermite differential equation is given by \( y'' - 2xy' + \lambda y = 0 \). Rewrite this equation in self-adjoint form. From the Sturm-Liouville form obtained, verify that the differential operator is self-adjoint on \((-\infty, \infty)\). Give the integral form for the orthogonality of the eigenfunctions.
Transcribed Image Text:**5.** The Hermite differential equation is given by \( y'' - 2xy' + \lambda y = 0 \). Rewrite this equation in self-adjoint form. From the Sturm-Liouville form obtained, verify that the differential operator is self-adjoint on \((-\infty, \infty)\). Give the integral form for the orthogonality of the eigenfunctions.
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