The function $x_2(t)$ determined by the initial value problem

$x_1^{\text{'}}=x_2$

$x_2^{\text{'}}=-x_1$

with initial conditions $x_1(0)=1$ and $x_2(0)=1$ is given by

Select one:

a$.x_2(t)=sintcost$

b$.x_2(t)=\frac{1}{2}(e^t{e}^{-t})$

c$.x_2(t)=-sintcost$

d$.x_2(t)=cost$