  The problem of algebraic dependence of solutions to (non-linear) first order
autonomous equations over an algebraically closed field of characteristic zero
is given a `complete' answer, obtained independently of model theoretic results
on differentially closed fields. Instead, the geometry of curves and
generalized Jacobians provides the key ingredient. Classification and formal
solutions of autonomous equations are treated. The results are applied to
answer a question on $D^n$-finiteness of solutions of first order differential
equations.
