The equation $$b_n(x)\frac{\mathrm{d}^ny}{\mathrm{d}x^n}+b_{n-1}(x)\frac{\mathrm{d}^{n-1}y}{\mathrm{d}x^{n-1}}+\ldots+b_1(x)\frac{\mathrm{d}y}{\mathrm{d}x}+b_0(x)y=R(x)$$
is a nonhomogeneous linear differential equation if $R(x)\ne 0$. I want to refer to the function $R(x)$ without writing down the whole equation. I want to say something like "If the (blank) in a linear differential equation is not zero, then it is a nonhomogeneous LDE." What term can I use?
This is usually called the forcing function. Although this word is usually used when the dependent variable is time, the meaning should be clear in your slightly more abstract context.