$\displaystyle y''+2y'+5y=\left\{\begin{array}{cc}0,&\mbox{ if }
t\leq t\leq\frac{\pi}{2}\\1, & \mbox{ if } t>\frac{\pi}{2}\end{array}\right$
where $\displaystyle y(0)=0, y'(0)=0 $
Alternatively, you can use the cases environment, which is designed for this purpose. Notice that it aligns items to the left (which is how printers set such expressions) instead of centering them.
$\displaystyle y''+2y'+5y=\begin{cases}0&\text{if }
t\leq t\leq\frac{\pi}{2},\\1 & \text{if } t>\frac{\pi}{2},\end{cases}$