I'd recommend
\left\{
\begin{array}{l}
{d^2x \over dt^2}
+ ( {{A+B} \over r^2} + {C \over r''^2} ) x
+ C ( {1 \over r'^2} - {1 \over r''^2} ) x' = 0,\\
{d^2y \over dt^2}
+ ( {{A+B} \over r^2} + {C \over r''^2} ) y
+ C ( {1 \over r'^2} - {1 \over r''^2} ) y' = 0,\\
{d^2z \over dt^2}
+ ( {{A+B} \over r^2} + {C \over r''^2} ) z
+ C ( {1 \over r'^2} - {1 \over r''^2} ) z' = 0;
\end{array}
\right.
for your example from one-page.html
The "\left\{" makes a stretchy brace on the left, and the "\right." makes a matching delimiter that is blank (\left and \right must come in pairs). The "\begin{array}{l}" starts an array with one column that is left-justified, and it ends at "\end{array}". The rows are searpated by "\\". (If you had more than one column, the entries in a row would be separated by "&".)
See Carol Fisher's excellent list of macros and examples for more information on what macros are available in TeX and how to use them.
Davide