Consider the following initial value problem:

$y^{\text{'}\text{'}}+6y^{\text{'}}+13y=(t-)$;$,y(0)=1,y^{\text{'}}(0)=0$

$ay(t).$

NOTE: Denote the Heaviside function $by{u}_c(t)$ where $u_c(t)=1iftc$ and $0$

otherwise. Indicate separately the exact value $ofc.$

$y(t)=\frac{1}{2}{u}_{}(t)e^{-3(t-)}sin(2t)+e^{-3t}cos(2t)+\frac{3}{2}{e}^{-3t}sin(2t)$

where $c=$

$by(t).$