Samuelson Acceleration Model Question
There is nothing more to it than the equation

$$Y_t - (c_y+v)Y_{t-1} = C^a + I^a$$

This is a linear non-homogeneous first-order difference equation, and it is non-homogeneous because there is a non-zero constant, $C^a + I^a \neq 0$. 

This is not some "habit in economics", but rather standard mathematical terminology.