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Binet's equation is $$\frac{d^2u}{d\theta^2}+(1-\frac{\lambda}{a^2v^2})u=0$$
I need to show that for $\lambda=a^2v^2$ path will be a circle.
For $\lambda=a^2v^2$ I have $$\frac{d^2u}{d\theta^2}=0$$

Can you give me some hints what to do now?

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Convert from Polar Coordinates to Rectangular! You are being fooled by the form of the second equation in your post. – Pieter Geerkens Aug 26 '13 at 22:34
What are Rectangular Coordinates? Cartesian maybe? I'm not sure if I know how to convert them. May you help me? – gov Aug 26 '13 at 22:57
See here. – Mhenni Benghorbal Aug 27 '13 at 0:29
Also, check this. – Mhenni Benghorbal Aug 27 '13 at 0:35
I checked both but I am not sure what are you telling me to do. Maybe I should solve inverse problem? – gov Aug 27 '13 at 9:39

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