Use Laplace transforms to solve the following initial value problem

$x^{dd}+x=u(t-1),x(0)=1,x^0(0)=0$

Here $u(t)$ is the Heaviside $($unit step$)$ function. The following Laplace transform formulas and some partial fractions are provided for your convenience:

$L\{coskt\}=\frac{s}{s^2+k^2},L\{sinkt\}=\frac{k}{s^2+k^2},L\{f(t-a)u(t-a)\}=F(s)e^{-as}$

$\frac{k^2}{s(s^2+k^2)}=\frac{1}{s}-\frac{s}{s^2+k^2}.$