How to solve a complex differential equation using the chain rule?

[newcool]

From a physics problem I obtained this differential equation.
$$\frac{d^3x}{dt^3} =-2(\frac{dx}{dt})^3$$

Would appreciate any tips on how to solve it as I have no idea on how to start.Thanks for the help

 

[Physics Monkey]

Ugh! Hint: try multiplying both sides by $$\frac{d^2 x}{dt^2}$$ and see what you can do.

 

[newcool]

$$1 =-2\frac{d^2 x}{dt^2}*(\frac{dx}{dt})^2$$ ??

I have only covered up to integration in calculus.

 

[Physics Monkey]

Just use the chain rule. For example, what is $$\frac{d}{dt}\left( \frac{1}{2} \left(\frac{d^2 x}{dt^2} \right)^2 \right) \,\,?$$