A First Look at Differential Algebra

John H. Hubbard (1, 2) , Benjamin E. Lundell (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 Department of Mathematics [Cornell]

The object of the paper is to prove that the differential equation u ′ (t) = t − [u(t)] 2 has no solutions which can be written using elementary functions, or anti-derivatives of elementary functions, or exponentials of such anti-derivatives, or anti-derivative

Mots clés: first look differential algebra; elementary function; differential equation

Domaines: Systèmes dynamiques [math.DS]

John H. Hubbard, Benjamin E. Lundell. A First Look at Differential Algebra. The American Mathematical Monthly, 2011, 118 (3), pp.245-261. ⟨10.4169/amer.math.monthly.118.03.245⟩. ⟨hal-01297702⟩