- #1

N00813

- 32

- 0

## Homework Statement

Given the ODE:

[tex] (1-x^2) \frac{d^2y}{d^2x} - x \frac{dy}{dx} + n^2 y = 0[/tex]

and that the weight function of the differential operator [tex] -(1-x^2) \frac{d^2y}{d^2x} + x \frac{dy}{dx} [/tex] is [tex] w = \frac{1}{\sqrt{1-x^2}} [/tex] to turn it into an SL operator, prove that:

[tex] \int_{-1}^{1} \frac{dy_m}{dx} \frac{dy_n}{dx} \sqrt{1-x^2} dx = 0 [/tex]

where [tex] y_m [/tex] and [tex] y_n [/tex] are orthogonal eigenfunctions of the ODE.

## Homework Equations

All above.

## The Attempt at a Solution

I attempted integration by parts of the LHS of the proposition, but that didn't seem to go anywhere.

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