When any three solutions are independent

Given an algebraic differential equation of order greater than one, it is shown that if there any nontrivial relation amongst number distinct nonalgebraic solutions, along with their derivatives, then already such a between three solutions. In the autonomous situation when over constant parameters assumption be one can dropped, and exists two These theorems are deduced as application following model-theoretic result: Suppose $p$ stationary type in theory differentially closed fields characteristic zero; realisations independent minimal. If constants minimality (and complete disintegratedness) follow from knowing independent. An algebro-geometric formulation terms $D$-varieties given. The same methods yield also analogous statement about families compact K\"ahler manifolds.