Nonlinear Differential Equation

The Question is:

Solve the following equation. The constant $\displaystyle \mu$ is non negative and $\displaystyle h$ is greater than zero.

$\displaystyle { ( \frac{dr}{dt} ) }^2 = \frac{2\mu}{r} + 2h$

Any help would be apperciated as I'm not entirely sure where to start with this problem.

Re: Nonlinear Differential Equation

Most likely, solution looks like:

$\displaystyle \frac{\mu \text{Log}\left[h \sqrt{r}+\sqrt{h} \sqrt{\mu +h r}\right]}{h^{3/2}}-\frac{\sqrt{r} \sqrt{\mu +h r}}{h} = \pm \sqrt{2} t+\text{C1}$(Lipssealed)

Re: Nonlinear Differential Equation

Hi Assassin0071 !

In fact, it is an ODE with separable variables :

dr/dt = sqrt((2m/r)+2h) = sqrt((2m+2hr)/r)

dt = dr/sqrt(r/(2m+2hr))

Then, integrate it.