It is homogeneous, because there are no functions present that do not depend on x1 or x2. Here's an inhomogeneous system: x_1' = x_2 + t and x_2'=-25x_1+10x_2.
After working on a problem, I found out the system to be: x_1' = x_2 and x_2'=-25x_1+10x_2. I can figure out this is autonomous because the right side of the equation does not explicitly depend on the variable t. But how do reason whether it's homogeneous or not? Thanks.