  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.
