Originally Posted by

**Ackbeet** I don't think your working is correct, because I don't think you can assume the equality holds. **Is k positive?** If so, why not do this:

$\displaystyle \dot{r}>\frac{k}{\sqrt{r}}$

$\displaystyle \sqrt{r}\,\dot{r}>k$

$\displaystyle \int\sqrt{r}\,\dot{r}\,dt>k\int dt$

$\displaystyle \int r^{1/2}\,dr>kt+C$

and so on. The end result is very like what you got, except that all the steps here are valid (I think), whereas, like I said, I don't think you can assume that the equality holds which gives you your differential **eq**uation.