Consider the following linear autonomous vector field on the plane:
$$ \left( \begin{array}{ccc} \dot{x_1}\\ \dot{x_2} \end{array} \right) = \left( \begin{array}{ccc} 0&1\\ 0&0 \end{array} \right) \left( \begin{array}{ccc} x_1\\ x_2 \end{array} \right), (x_1(0),x_2(0))=(x_{10},x_{20}) $$
Describe the invariant sets and determine whether the origin is stable or unstable.
The answer states that $\dot{x_1}=x_2$ and $\dot{x_2}=0$ implies $x_1(t)=x_{20}t+x_{10}$ and $x_2(t)=x_{20}$. Every horizontal line is an invariant set and that $(x_1,x_2)=(0,0)$ is unstable.
Can someone explain to me how did they get the expression for $x_1(t)$, and I'm not sure how to deduce the invariant sets for this as well.