How do you make numbered equations in latex?

You can use display math environment such as equation:

Notes:

• The d in dt should be upright as d is an operator, not a variable. Have defined a macro for that and corrected it below.

References:

• You should not use a the TeX way of using a $$ to enter display math. See Why is \[ ... \] preferable to $$ ... $$?

• An excellent reference for math mode is Herbert Voss' comprehensive review of mathematics in (La)TeX.

Code:

\documentclass{article} 

\newcommand{\dd}[1]{\mathrm{d}#1}

\begin{document}

\begin{equation}
\ddot{\underline{\mathbf{r}}} = \frac{\dd{}{^2}\underline{\mathbf{r}}}{\dd{t}^2} = 0
\end{equation}
\end{document}

You can also use the align environment:

\documentclass[a4paper,11pt]{article}
%\documentclass[a4paper,11pt]{scrartcl}
\usepackage{amsmath} 
\usepackage[utf8]{inputenc}

\begin{document}
%Equations with numbering
\begin{align}
\ddot{\underline{\mathbf{r}}} &= \frac{d{^2}\underline{\mathbf{r}}}{dt^2}\\
                              &= 0
\end{align} 

%Equations with no numbering in specific line by using \nonumber
\begin{align}
\ddot{\underline{\mathbf{r}}} &= \frac{d{^2}\underline{\mathbf{r}}}{dt^2}\nonumber\\
                              &= 0
\end{align}

%Equations without numbering
\begin{align*}
\ddot{\underline{\mathbf{r}}} &= \frac{d{^2}\underline{\mathbf{r}}}{dt^2}\\
                              &= 0
\end{align*} 
\end{document}