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Solving Abel first order differential equation

First and Second kind
\(y'=f_0 + f_1 y + f_2 y^2 + f_3 y^3\)

Nasser M. Abbasi       June 24, 2025 at 8:57pm

1.1 introduction
1.2 Algorithm
1.3 About equivalence between two Abel ode’s
1.4 Examples
1.5 Abel second kind \(\left ( g_{1}y+g_{0}\left ( x\right ) \right ) y^{\prime }=f_{0}+f_{1}y+f_{2}y^{2}+f_{3}y^{3}\)
1.6 Converting Abel first kind ode with non constant invariant to canonical form \(u^{\prime }\left ( \xi \right ) =F\left ( \xi \right ) u^{3}\left ( \xi \right ) \)
1.7 Converting Abel first kind to second kind