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The solution $x(t), t \geq 0$, to the differential equation $\ddot{x}=-k \dot{x}, k>0$ with initial conditions $x(0)=1$ and $\dot{x}(0)=0$ is

  1. $x(t)=2 e^{-k t}+2 k t-1$
  2. $x(t)=2 e^{-k t}-1$
  3. $x(t)=1$
  4. $x(t)=2 e^{-k t}-k t-1$
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