$2.(25$ points$)$ Use the Laplace Transform to solve the initial value problem:

$y^{\text{'}\text{'}}+2y^{\text{'}}+2y=2t,y(0)=2,y^{\text{'}}(0)=-7$

After your complete work and finding the answer, choose the right answer from the following possible answers:

a$.,y(t)=t-1+e^{-t}(3cos(t)-5sin(t))$

b$.,y(t)=1-t+e^{-1}(5cos(t)-3sin(t))$

c$.,y(t)=1+t+e^{-1}(5cos(t)+3sin(t))$

d$.$ None of the above