Consider the initial value problem

$$y$=[13$t$2$t$0]$y$+$g$($t$),$y$(1)=[44].$y$=[1$t$3$t$20]$y$+$g$($t$),$y$(1)=[44].$

Suppose we know that

$$y$($t$)=[2$t$+$$2$t$2+$$]$y$($t$)=[2$t$+$$2$t$2+$$]$

is the unique solution to this initial value problem. Find g$($t$)$g$($t$)$ and the constants and $.$