ordinary differential equations

Consider ordinary differential equations given by ẋ₁(t) = 2x₂(t) ẋ₂(t) = r(t) with initial conditions x₁(0) = 1 and x₂(0) = 0. If r(t) = {1, t ≥ 0; 0, t < 0}, then at t = 1, x₁(t)...

Consider ordinary differential equations given by $\dot{x}_1(t)=2 x_2(t), \dot{x}_2(t)=r(t)$ with initial conditions $x_1(0)=1$ and $x_2(0)=0$. If $r(t)=\left\{\begin{array}{ll}1,...