Complex sentence: It does not matter if nonlinear known functions appear in the equations; in particular, a differential equation is linear if it is linear in the unknown function and its derivatives, even if non linear known functions appear as coefficients.
Split into simpler sentences: It does not matter if nonlinear known functions appear in the equations. In particular, a differential equation is linear if the undefined function and its derivatives are linear, even if nonlinear, defined functions appear as coefficients.