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

this is not from a math course, but from Gregory's classical mechanics book prob 2.10

it's easy to obtain the desired ODE

[tex]\dot{r}^{2}=\frac{u^{2}}{a^{2}}(\frac{U^{2}a^{2}}{a^{2}}-r^{2})[/tex]

since it's non-linear, i have a difficult time to solve for r(t)

u, U and a are some constants with unit speed, speed and length resp.

2. Relevant equations

3. The attempt at a solution

all methods i know fail, I believe there is some trick that I am not aware of. great appreciate for any help:(

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# Homework Help: Solving ODE involving square of first derivative

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