Take the Laplace transform of the IVP $$\frac{dy}{dt}-y=-6\cos( kt), y(0) = 2$$ Use $Y$ for the Laplace transform of $y$, (not $Y(s)$).



So

$Y =$

$\hskip 30pt -6 s$ -----------------------------

$+$

$\hskip 8pt 2$ ------------

$\hskip 10pt =$

$s$$+$ -------------------------------------------------------------- $\hskip 70pt s^2+k^2$

$+$

----------------------------------- $\hskip 35pt s-1$

and $y(t) =$