A differential analog of Noether's normalization lemma

Noether's normalization lemma says that for every affine variety of dimension $d$ there exists a surjection to a $d$-dimensional affine space. One can interpret this lemma as follows. Let a system of algebraic equations defining a $d$-dimensional variety be given. Then there exists a change of variables such that if one fixes first $d$ variables, after this change the system is solvable. In the talk we will discuss analogs of this statement for differential equations. In particular, we prove that for any differentially algebraic variety of dimension $d$ there exists a surjection onto an affine space. We interpret this fact as a statement about a change of variables in a differential equation.