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**1. The problem statement, all variables and given/known data**

Express the DE as a first order system normal form. Then, express is matrix notation.

2y''+3y'-4ty=1-t^3

I need to transform this into a first order system. I first divided the entire equation by 2 and got

y''-(3/2)y'-2ty=(1-t^3)/2

I am not sure what to do now.

My first attempt was setting x1=y, x1'=y', and x2=y', x2'=y''

I don't know if I am heading in the right direction and if so, was not sure what to do next.