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**[SOLVED] Transforming 3rd order D.EQ into 1st order**

## Homework Statement

Transform the following diff eq into a system of first order diff eqs.

2y''' - 6y'' - y' + 3y =t^4cos(2t)

## The Attempt at a Solution

heres what I've done so far:

y =A A'=y'

y' =B B'=y''

y'' =C C'=y'''=6y'' + y' - 3y + t^4cos(2t)

C'=-3A + B + 6C +t^4cos(2t)

B'= C

A'= B

I don't know if this is correct because the initial D.Eq is not homogenous, don't know what to do with the t^4cos(2t)