Abel equation of the first kind
In mathematics, an Abel equation of the first kind, named after Niels Henrik Abel, is any ordinary differential equation that is cubic in the unknown function. In other words, it is an equation of the form
The substitution brings the Abel equation of the first kind to the "Abel equation of the second kind" of the form
brings the Abel equation of the first kind to the canonical form
- E. Panayotounakos, Dimitrios; Theodoros I. Zarmpoutis (29 August 2011). "Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs of the First Kind and Relative Degenerate Equations)". International Journal of Mathematics and Mathematical Sciences Volume 2011 (2011) 2011: 13. doi:10.1155/2011/387429. PMID 387429.