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ODE Substitution: Solving Bessel Equation with x=cosθ
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[QUOTE="Jerbearrrrrr, post: 3220283, member: 225436"] 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. [b]Could someone just verify that the question is right, please?[/b] 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). [/QUOTE]
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ODE Substitution: Solving Bessel Equation with x=cosθ
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