Given the continuous time dynamical system with the rule depending on time: $$x'=3x+(2-t)y\qquad y'=xy-t$$ create a new system which is equivalent to the above system for which the rule does not depend on $t$.
My solution so far: I recognize that this can be written in matrix for as in $Y'=AY$
|Y'| = |x'| = |3 2t| * |x|
|y'| |y -t/y| |y|
I'm stuck here because I get the feeling my A shouldn't include any variables, so I tried to solve the DEs. I start with $y'=xy-t$:
$y'=xy-t$
$y'-xy=-t$
multiply by $u(t)=e^{-xt}$
d(ye^-(xt))/dt=-te^-(xt)
ye^-(xt)=[e^(xt)(1-xt)]/x^2
y=[e^(2xt)(1-xt)]/x^2
Then I'm stuck here but I'm pretty sure this isn't the way to go.