Geometric triviality conjecture for generic differential equations

Let $f(x)$ be a generic differential equation of fixed order $h>1$ and fixed degree $d>1$, and let $a$ and $b$ be two solutions of $f$. Geometric triviality conjecture. Any two solutions of a generic differential equation of fixed order and degree greater than one are differentially algebraically independent. This is proposed as a strong form of geometric triviality in the Zilber trichotomy for strongly minimal sets; a general classification of geometrically trivial strongly minimal sets in differentially closed fields is not known.