Suppose that I have the following set of 2 equations:
$\frac{d(x(t))}{dt} = 5tx(t) + 2y(t)$
$\frac{d(y(t))}{dt} = 5ty(t)+2x(t)$
I have read that this is a system of "Linear first order non-constant coefficient homogeneous" differential equations. I understand everything except the homogeneous part.
I understand that if you have something like:
$M(x,y)dx + N(x,y)dy = 0$ then this equation is homogeneous if $M$ and $N$ are both homogeneous functions of the same degree but I don't really know how to apply this definition to the set of equations I wrote above.
So, in general, how to tell if a system of ordinary differential equations is homogeneous?