4820 Ordinary Differential Equations, Solution and Reduction 4820 



Equations. 



Fuss, N. [1818] St Pet. Ac. Sc. Mm. 9 (1824) 



115-. 

 Besge, V. A. Liouv. J. Mth. 4 (1859) 72; 18 



(1873) 139-. 



Frahm, W. [1873] Mth. A. 8 (1875) 35-. 

 Le Paige, C. M. M. H. H. (xn) Brux. S. Sc. 



A. 1 (1877) (Pt. 2) 51-. 

 Tanner, H. W. I.. [1877] Mess. Mth. 7 (1878) 



107-. 

 Lindman, C. F. Stockh. Ofv. 37 (1880) 



No. 1, 3-. 

 Harley,E. QJ. Mth. 17 (1881) 352- ; 18(1882) 



41-. 



Poincare, H. C. E. 98 (1884) 793-. 

 Sharpe, H. J. Mess. Mth. 13 (1884) 66-. 

 Jamet, V. C. E. 104 (1887) 844-. 

 Guldberg, A. C. E. 117 (1893) 614-. 

 Chini, M. Tor. Ac. Sc. At. 34 (1898) 56-. 

 adjoint to equation, nth order. Grilnfeld, E. 



Crelle J. Mth. 122 (1900) 43-, 88. 

 with algebraic integral. Brioschi, F. Mil. I. 



Lomb. Ed. 9 (1876) 786- ; 10 (1877) 48-. 



arbitrary parameter. Picard, E. C. E. 118 

 (1894) 760- . 



class. Liouville, J. Liouv. J. Mth. 6 (1841) 



448. 

 . Boole, G. (vi Adds.) Ph. Mg. 30 (1847) 



96-. 

 class. Eosanes, J. Z. Mth. Ps. 16 (1871) 



263-. 



. Jablonski, E. As. Fr. C. E. (1877) 188-. 

 . Haag, . Par. S. Mth. Bll. 8 (1880) 



80-. 

 . Catalan, E. Brux. Ac. Bll. 12 (1886) 



. Vessiot, E. Par. EC. Norm. A. 10 (1893) 



53- ; C. E. 116 (1893) 959-, 1112-. 

 . Lindhagen, A. N. Ts. Mth. 10 (B) (1899) 



35- ; Fschr. Mth. (1899) 297. 

 reducible to linear equations. Appell, . 



C. E. 107 (1888) 776-. 

 with complete differentials, two systems. 



Stodoikiewicz, A. J. Krk. Ak. (Mt.-Prz.) 



Pam. 12 (1886) (93)-; Fschr. Mth. (1886) 



307. 

 connected with orthogonal trajectories. Euler, 



L. [1781] St Pet. Ac. Sc. Mm. 11 (1830) 



125-. 

 of 1st degree. Trembley, J. Turin Mm. Ac. 



(1790-91) 1-. 



2nd degree. Fuss, N. [1819] St Pet. Ac. 

 Sc. Mm. 11 (1830) 258-. 



. Enneper, A. Schlomilch Z. 8 (1863) 



58-. 

 , general integral of which is uniform. 



Painleve, P. C. E. 117 (1893) 211-. 



form y m = x m (Ax-y" + Bxy' + Cy). Spitzer, 

 S. Arch. Mth. Ps. 58 (1876) 100-. 



with fractional indices. Besge, V. A. Liouv. 



J. Mth. 9 (1844) 294. 

 general integral of which is linear fractional 



function of arbitrary constants. Wallenberg, 



G. Crelle J. Mth. 121 (1900) 210-. 

 geometrical interpretation. Fouret, G. C. E. 



102 (1886) 415-. 



having fundamental system of integrals. Guld- 

 berg, A. C. E. 116 (1893) 964-. 

 . Lie, S. C. E. 116 (1893) 



1233-. 

 integrated by differentiation. Eaffy, L. Par. 



S. Mth. Bll. 23 (1895) 50-. 

 invariant under transformation xx' = l, yx'=y'. 

 . Elliott, E. B. Mess. Mth. 19 (1890) 7-. 

 not containing the independent variable. 



Zehfuss, G. (xi) Z. Mth. Ps. 3 (1858) 



247-. 

 occurring in Laplace's kinetic theory of tides. 



Ling, G. H. A. Mth. 10 (1895-96) 95-. 

 of multiplier. Genocchi, A. Mil. I. Lomb. 



Ed. 10 (1877) 553-. 



1st order. Liouville, R. C. E. 103 (1886) 

 476- ; 106 (1888) 1648- ; Par. EC. Pol. J. 62 

 (1893) 181-. 



. Vessiot, . C. E. 116 (1893) 427-. 



. Korkine, A. C. E. 122 (1896) 1183- ; 



123 (1896) 38-, 139; Mth. A. 48 (1897) 317-. 

 . Petrovitch, M. C. E. 122 (1896) 



1261-. 

 . Painlere, P. C. E. 122 (1896) 



1319- ; 123 (1896) 88-. 



. Cahen, A. C. E. 127 (1898) 1196-. 



. Horn, J. Mth. A. 51 (1899) 360-. 



, class, and invariant formations at- 

 taching to them. Liouville, E. C. E. 105 

 (1887) 460-, 496. 



,2 variables. Ermakov, V. P. Fschr. 



Mth. (1887) 316-. 

 and 2nd orders, 2 variables. Weiler, A. 



Grunert Arch. 29 (1857) 1-. 



2nd order. Besge, V. A. Liouv. J. Mth. 

 9 (1844) 336. 



. Hazzidakis, J. N. [1880] Crelle J. 



Mth. 90 (1881) 74-. 

 . Guldberg, A. N. Ts. Mth. 7 (B) 



(1896) 1-; Fschr. Mth. (1896) 250. 

 , with fixed critical points. Painleve, P. 



C. E. 126 (1898) 1185-, 1697-. 



3rd order. Goursat, E. C. E. 98 (1884) 

 419-. 



. Klein, F. Mth. A. 23 (1884) 587-. 



. Kummer, E. E. Crelle J. Mth. 100 



(1887) 1-. 



4th order. Pochhammer, L. Crelle J. Mth. 

 104 (1889) 116-. 



with periodic coefficients, series attached to 



theory of. Liapouno/, A. C. E. 123 (1896) 



1248-. 

 possessing fundamental integrals. Lie, S. 



Leip. Mth. Ps. B. 45 (1893) 341-. 

 relating to breaking of railway bridges. Stokes, 



G. G. Camb. Ph. S. T. 8 (1849) 707-. 



Euler's factor. Lorenz, L. V. (xn) Ts. Mth. 



3 (1873) 174- ; 4 (1874) 33-. 



. Heun, K. Mth. A. 31 (1888) 363-. 



. , application. Peterson, J. Mth. Ts. 4 



(1862) 139-. 

 and Poisson's equations. L6vy, L. N. A. 



Mth. 8 (1889) 545-. 

 Exact differential. Autonne, L. N. A. Mth. 



15 (1896) 232-. 



358 



