Equations differentielles sur les hypersurfaces de l'espace projectif complexe de dimension 4

The main goal of this work is to prove that every entire curve in a smooth hypersurface of degree greater than or equal to 97 in the complex projective space of dimension 4 must satisfy an algebraic differential equation of order 3. A logarithmic version of this result is given proving that every entire curve in the complement of a smooth surface of degree greater than or equal to 92 in the complex projective space of dimension 3 must satisfy an algebraic differential equation of order 3.