Question

Find eigenvalues of $x^2 \frac{d^2\phi}{dx^2} + x \frac{d\phi}{dx} + \lambda \phi = 0$ with boundary conditions $\phi(1) = \phi(b) = 0$

score 189 · Answer 1 · 2019-10-30 06:17:38

189

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Find eigenvalues of $x^2 \frac{d^2\phi}{dx^2} + x \frac{d\phi}{dx} + \lambda \phi = 0$ with boundary conditions $\phi(1) = \phi(b) = 0$

Published on 30 Oct 2019 - 6:17

score 1k · Answer 2 · 2026-03-26 03:19:09

1k

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Determining Weight function in Sturm Liouville problem

Published on 26 Mar 2026 - 3:19

score 267 · Answer 3 · 2026-03-26 04:52:25

267

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Show that eigenvalues are non-negative from the two-dimensional Rayleigh Quotient

Published on 26 Mar 2026 - 4:52

score 174 · Answer 4 · 2026-02-23 13:30:20

174

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By changing the variable in the φ equation to x = cos φ, derive the self adjoint form of the Legendre equation

Published on 23 Feb 2026 - 13:30

score 901 · Answer 5 · 2026-03-26 06:30:07

901

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Consider the Sturm-Liouville problem $y^{\prime\prime}+ \lambda y=0,y(0)=y( \pi)=0.$

Published on 26 Mar 2026 - 6:30

score 537 · Answer 6 · 2019-12-08 04:09:36

537

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How do I apply sturm comparison theorem to draw the conclusion?

Published on 08 Dec 2019 - 4:09

score 563 · Answer 7 · 2019-12-11 23:33:00

Find the expansion of $f (x) = x, 0 ≤ x ≤ \pi$ in a series of eigenfunctions of the Sturm–Liouville system $y''+\lambda y = 0, y (0) = 0, y (\pi)=0.$

score 42 · Answer 8 · 2026-03-27 00:59:50

42

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Let $P_n(x)$, $n=0,1,2,...$ be an infinite set of polynomials satisfying the three conditions

Published on 27 Mar 2026 - 0:59

score 161 · Answer 9 · 2026-03-27 00:58:45

161

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show directly that the eigenfunction of the given Sturm-Liouville problem are orthogonal

Published on 27 Mar 2026 - 0:58

score 108 · Answer 10 · 2020-01-13 18:15:04

108

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Verify that the periodic Sturm- Liouville system has a symmetric operator

Published on 13 Jan 2020 - 18:15

score 37 · Answer 11 · 2020-01-13 19:53:46

37

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show that $λ=0$ is an eigenvalue of the regular Sturm- Liouville system

Published on 13 Jan 2020 - 19:53

score 155 · Answer 12 · 2020-01-14 17:09:49

155

Views

Show that the function is orthogonal

Published on 14 Jan 2020 - 17:09

score 123 · Answer 13 · 2020-01-22 11:29:16

123

Views

Solving PDE with interesting initial condition

Published on 22 Jan 2020 - 11:29

score 88 · Answer 14 · 2020-01-23 15:30:52

88

Views

example of Sturm-Liouville problem with Lu=u'' differential operator

Published on 23 Jan 2020 - 15:30

score 48 · Answer 15 · 2020-01-23 17:36:23

48

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Sturm-Liouville exercise: finding linearly independent solutions

Published on 23 Jan 2020 - 17:36

List Question

Find eigenvalues of $x^2 \frac{d^2\phi}{dx^2} + x \frac{d\phi}{dx} + \lambda \phi = 0$ with boundary conditions $\phi(1) = \phi(b) = 0$

Determining Weight function in Sturm Liouville problem

Show that eigenvalues are non-negative from the two-dimensional Rayleigh Quotient

By changing the variable in the φ equation to x = cos φ, derive the self adjoint form of the Legendre equation

Consider the Sturm-Liouville problem $y^{\prime\prime}+ \lambda y=0,y(0)=y( \pi)=0.$

How do I apply sturm comparison theorem to draw the conclusion?

Find the expansion of $f (x) = x, 0 ≤ x ≤ \pi$ in a series of eigenfunctions of the Sturm–Liouville system $y''+\lambda y = 0, y (0) = 0, y (\pi)=0.$

Let $P_n(x)$, $n=0,1,2,...$ be an infinite set of polynomials satisfying the three conditions

show directly that the eigenfunction of the given Sturm-Liouville problem are orthogonal

Verify that the periodic Sturm- Liouville system has a symmetric operator

show that $λ=0$ is an eigenvalue of the regular Sturm- Liouville system

Show that the function is orthogonal

Solving PDE with interesting initial condition

example of Sturm-Liouville problem with Lu=u'' differential operator

Sturm-Liouville exercise: finding linearly independent solutions

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