Geodesic
Fiber preserving transformations and the equation \(y'''=f(x,y,y',y'')\)
Electronic journal of differential equations, Tome 2005 (2005)
In this paper, we give simple explicit conditions for a third order ordinary differential equation to be equivalent to the equations $y'''=0$ and $y'''+y=0$ under fiber preserving transformations.
Classification : 58A15, 58A17, 58A20
Keywords: Cartan's method, equivalence problem, fiber preserving transformations 
@article{EJDE_2005__2005__a182,
     author = {Dridi,  Raouf and Neut,  Sylvain},
     title = {Fiber preserving transformations and the equation \(y'''=f(x,y,y',y'')\)},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1076.34053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a182/}
}
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Dridi,  Raouf; Neut,  Sylvain. Fiber preserving transformations and the equation \(y'''=f(x,y,y',y'')\). Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a182/