  We study families of linear differential equations parametrized by an
algebraic variety $\mathcal{X}$ and show that the set of all points $x\in
\mathcal{X}$, such that the differential Galois group at the generic fibre
specializes to the differential Galois group at the fibre over $x$, is Zariski
dense in $\mathcal{X}$. As an application, we prove Matzat's conjecture in full
generality: The absolute differential Galois group of a one-variable function
field over an algebraically closed field of characteristic zero is a free
proalgebraic group.
