Geodesic
Nonlinear fourth-order differential equations with solutions in the form of transcendents
Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 72-87

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We present two hierarchies of ordinary differential equations and give the relations between these hierarchies. We find rational and special solutions of one hierarchy. Solutions of two differential equations are shown to be essentially transcendental functions with respect to the integration constants. 
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     author = {N. A. Kudryashov},
     title = {Nonlinear fourth-order differential equations with solutions in the form of transcendents},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {72--87},
     publisher = {mathdoc},
     volume = {122},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a6/}
}
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N. A. Kudryashov. Nonlinear fourth-order differential equations with solutions in the form of transcendents. Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 72-87. http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a6/