$\frac{d^2x}{dt^2} =3.$ Separation of variables Can someone show the steps to desperate the values and do the integration for the following: $$\frac{d^2x}{dt^2} =3\quad?$$
What I have is 
$$d^2x=3dt^2$$
Integrate 
$$dx=3t^2 + c$$
$$x=t^3+ct +d$$
Is that right?

I assume you mean
\begin{align}
\frac{d^2x(t)}{dt^2}=3
\end{align}
You don't really need seperation of variables. Simply integrate twice.
First integration yields
\begin{align}
\frac{dx(t)}{dt}=\int3\,dt = 3t+c
\end{align}
Integrate again to obtain
\begin{align}
x(t) = \int 3t+c\, dt = \frac32t^2+ct+d
\end{align}
Your error was, that from $d^2x = 3dt^2$ it follows $dx = (3t+c)dt$ and not $dx=3t^2+c$.
