Question

r=f(t)
r''=K/r^2
solve for f(t)

Answer 1

f(t) = r

Answer 2

:)

Answer 3

haha =[

Answer 4

hahahah... 100 for @zzr0ck3r

Answer 5

how about i solve it for small r increments, it wud be approximately linear ode there

Answer 6

What if you multiply by the first derivative:
\[\begin{align*}
\color{red}{r'}r''&=\frac{K\color{red}{r'}}{r^2}
\end{align*}\]
To get this equation, we would have differentiated the following with respect to \(t\):
\[\begin{align*}
\frac{1}{2}(r')^2&=C-\frac{K}{r}
\end{align*}\]
I suppose there's nothing stopping us from taking the square root, then we have
\[\begin{align*}
r'&=\pm\sqrt{2C-\frac{2K}{r}}
\end{align*}\]
I'm curious to see if there's a way to find \(r\) using a similar approach for reducing \(r''\) to \(r'\)...

Answer 7

hey thats very nice at least we can show that r' is converging now

Answer 8

the problem came out of a particle charge that is being repelled by a stationary charge