Consider ordinary differential equations given by
\[
\frac{dx_1(t)}{dt} = 2x_2(t), \quad \frac{dx_2(t)}{dt} = r(t)
\]
with initial conditions \( x_1(0) = 1 \) and \( x_2(0) = 0 \).
If
\[
r(t) = \begin{cases}
1, & t \geq 0 \\
0, & t < 0
\end{cases}
\]
then at \( t = 1 \), \( x_1(t) = \underline{2cm} \) (round off to the nearest integer).
