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Apparently this is a Bessel equation

[itex] \sin \theta \frac{d^2 y}{d\theta^2} + \cos \theta \frac{dy}{d\theta} + n(n+1)\sin \theta y = 0 [/itex]

after using x = cos\theta. The problem says use x = cos \theta anyway. A further substitution may be required, but is not alluded to. The variable 'x' is used in the 'target' equation too.

It's supposed to end up as

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

thanks

I don't remember seeing any qualifications about p (wasn't my question in the first place, just remembering it from a discussion today).

[itex] \sin \theta \frac{d^2 y}{d\theta^2} + \cos \theta \frac{dy}{d\theta} + n(n+1)\sin \theta y = 0 [/itex]

after using x = cos\theta. The problem says use x = cos \theta anyway. A further substitution may be required, but is not alluded to. The variable 'x' is used in the 'target' equation too.

**Could someone just verify that the question is right, please?**ie, that the substitution will give the following.It's supposed to end up as

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

thanks

I don't remember seeing any qualifications about p (wasn't my question in the first place, just remembering it from a discussion today).

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