Solve the initial value problem $\frac{dy}{dt}+3y=6$, $y\left(0\right)=1$.

$y\left(t\right)=e^{3t}-2$

$y\left(t\right)=2-e^{-3t}$

$y\left(t\right)=\frac{1}{3}(e^t+2)$

$y\left(t\right)=2e^t-1$