Abel equation of the first kind
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This article is about certain differential equations. For certain functional equations named after Abel, see Abel equation.
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
where . If and , or and , the equation reduces to a Bernoulli equation, while if the equation reduces to a Riccati equation.