$(25$ points$)$ Use Laplace Transform to solve the following initial value problem

$y^{\text{'}\text{'}}+y^{\text{'}}=2e^{3t},y(0)=-1,y^{\text{'}}(0)=4$

Choose the right answer from the following possible answers:

a$.$

b$.$

$y=\frac{7}{2}-\frac{7}{3}{e}^{3t}+\frac{1}{6}{e}^{-t}$

$c.y=\frac{7}{3}-\frac{7}{2}{e}^{-t}+\frac{1}{6}{e}^{3t}$

d$.$ None of the above