  Using the data schemes developed by Arrondo-Sols-Speiser, we give a rigorous
definition of algebraic differential equations on the complex projective space
$P^n$. For an algebraic subvariety $S \subseteq P^n$, we present an explicit
formula for the degree of the divisor of solutions of a differential equation
on $S$ and give some examples of applications. We extend the technique and
result to the real case.

Algebraic Geometry