Geodesic
Classifications of completely integrable implicit second order ordinary differential equations
Journal of Singularities, Tome 10 (2014), pp. 271-285

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An implicit second order ordinary differential equation is said to be completely integrable if there exists at least locally an immersive two-parameter family of geometric solutions on the equation hypersurface like as in the case of explicit equations. An implicit equation may have an immersive one-parameter family of geometric solutions (or, singular solutions) and a geometric solution (or, an isolated singular solution). In this paper, we give a classification of types of completely integrable implicit second order ordinary differential equations and give existence conditions for such families of solutions.
DOI : 10.5427/jsing.2014.10s
Classification : 34A26, 34A09, 34C05, 65L05 
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     author = {Masatomo Takahashi},
     title = {Classifications of completely integrable implicit second order ordinary differential equations},
     journal = {Journal of Singularities},
     pages = {271--285},
     publisher = {mathdoc},
     volume = {10},
     year = {2014},
     doi = {10.5427/jsing.2014.10s},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2014.10s/}
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Masatomo Takahashi. Classifications of completely integrable implicit second order ordinary differential equations. Journal of Singularities, Tome 10 (2014), pp. 271-285. doi: 10.5427/jsing.2014.10s

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