Solving a system of differential equations with the variable $x$
$$y'=\begin{pmatrix} 3x-1 & x-1 \\ -x-2 & x-2 \end{pmatrix}y$$ $$y'_1=(3x-1)y_1+(x-1)y_2$$ $$y'_2=(-x-2)y_1+(x-2)y_2$$ Sum both differential equations: $$(y_1+y_2)'=(2x-3)(y_1+y_2)$$ This DE is separable. I suppose that $\dfrac {dy}{dx}=y'$.