Need help transforming a Differential Equation

[bengaltiger14]

Homework Statement

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.

 

[HallsofIvy]

That can be done in a number of ways. The simplest is : Define u= y' so that y"= u' and your second order differential equation becomes a first order equation in y and u. You now have two first order equations.

 

[bengaltiger14]

So, when I rewrite the equation, do I leave out the 'y' in the term 2ty?

hence,
u'+(3/2)u-2=(1-t^3)/2