Write a differential equation for this description I'm still very new to differential equations and not sure if I'm understanding this question correctly:

If the velocity at time $t$ for a particle moving along a straight line
  is proportional to the fourth power of its position $x$, write a
  differential equation that fits this description.

So I think the equation would be:
$\frac{dt}{dx}=tx^4$
Is this correct?

Close. This is what you want:
$$
\frac{dx}{dt}(t)=\alpha x(t)^{4}\text{ where }\alpha\text{ is a constant}.
$$
$x(t)$ is the position of the particle at time $t$, from which it
follows that $\frac{dx}{dt}(t)$ is its velocity at time $t$. $\alpha$
appears in the above since the question asks the velocity to be proportional
to $x(t)^{4}$.
