Use the Laplace transform to solve for
y_(1)(t)
and
y_(2)(t)
that satisfies the coupled differential equation,
(d)/(dt)[[y_(1)],[y_(2)]]=[[-2,-1],[1,-2]][[y_(1)],[y_(2)]]+[[sin(t)],[cos(t)]]
with initial condition,
y_(1)(0)=1
y_(2)(0)=1
.