Liouvillian First Integrals of Differential Equations

  title={Liouvillian First Integrals of Differential Equations},
  author={Michael F. Singer},
Liouvillian functions are functions that are built up from rational functions using exponentiation, integration, and algebraic functions. We show that if a system of differential equations has a generic solution that satisfies a liouvillian relation, that is, there is a liouvillian function of several variables vanishing on the curve defined by this solution, then the system has a liouvillian first integral, that is a nonconstant liouvillian function that is constant on solution curves in some… CONTINUE READING
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