A DAE system of this form is called "semi-explicit". Every solution of the second half "g" of the equation defines a unique direction for "x" via the first half "f" of the equations, while the direction for "y" is arbitrary. But not every point "(x,y,t)" is a solution of "g". The variables in "x" and the first half "f" of the equations get the attribute "differential". The components of "y" and the second half "g" of the equations are called the "algebraic" variables or equations of the system. term "algebraic" in the context of DAEs only means "free of derivatives" and is not related to (abstract) algebra.