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Consider two solutions $x(t)=x_1(t)$ and $x(t)=x_2(t)$ of the differential equation $\dfrac{d^2x(t)}{dt^2}+x(t)=0, \: t>0$ such that $x_1(0)=1, \dfrac{dx_1(t)}{dt} \bigg \vert_{t=0}=0$, $x_2(0)=0, \dfrac{dx_2(t)}{dt}\bigg \vert _{t=0}=1$.

The Wronskian $W(t)=\begin{bmatrix} x_1(t) & x_2(t)\\  \\ \dfrac{dx_1(t)}{dt} & \dfrac{dx_2(t)}{dt} \end{bmatrix}$ at $t=\pi /2$ is

  1. $1$
  2. $-1$
  3. $0$
  4. $\pi /2$
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