(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A set of eigenfunctions y_{n}(x) satisfies the following Sturm-Liouville equation:

[itex] \frac{d(f(x)*y'_{m})}{dx}+\lambda*\omega*y_{m}=0[/itex]

with following boundary conditions:

[itex] \alpha_{1}y+\beta_{1}y'=0[/itex]

at x=a

[itex] \alpha_{2}y+\beta_{2}y'=0[/itex]

at x=b

Show that the derivatives u_{n}(x)=y'_{n}(x) are orthogonal functions.

Determine the weighting function for these functions.

What boundary conditions are required for orthogonality?

2. Relevant equations

Orthogonal functions:

[itex]\int(dx*\omega*y_{n}(x)*y_{m}(x)=0[/itex]

Integrate from a to b.

3. The attempt at a solution

I'm not sure how to start this problem, can someone point me in the right direction?

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# Homework Help: Orthogonality and Weighting Function of Sturm-Liouville Equation

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