4870 



Non-linear Differential Equations of First Order 



4870 



4870 General theory of ordinary 

 equations, not linear, of the 

 first order. 



Bugaev, N. V. (xn) Eec. Mth. (Moscou) 3 



(1868) (Ft. 1) 249-. 

 Painleve, P. C. B. 107 (1888) 221-, 320-, 



724- ; Par. EC. Norm. A. 8 (1891) 9-, 103-, 



201-, 267- ; 9 (1892) 9-, 101-, 283-. 

 Laurent, . Par. EC. Pol. J. 2 (1897) 1-. 

 Algebraic equations. Rosaries, J. Mth. A. 3 



(1871) 535-. 

 . Vivanti, G. Palermo Cir. Mt. Ed. 4 



(1890) 197-. 

 . Wallenberg, G. Crelle J. Mth. 116 



(1896) 1- ; 122 (1900) 155. 

 , 1st degree. Darboux, G. Bll. Sc. Mth. 



As. 2 (1878) 60-, 123-, 151-. 

 , , with algebraic general primitive. 



Pincherle, S. Mil. I. Lomb. Ed. 10 (1877) 



143-. 

 -, 2nd degree, in 2 variables with general 



algebraic integrals. Casorati, F. Mil. I. 



Lomb. Ed. 7 (1874) 846-. 



with general primitive. Casorati, F. 

 Em. E. Ac. Line. T. 1 (1877) 185-. 



integrals. Autonne, L. C. E. 115 (1892) 

 587-. 



Approximations to solution. Trembley, J, 



Turin Mm. Ac. (1790-91) 53-. 

 Binomial equation. Petrovitch, M. C. E. 



121 (1895) 632-. 

 Briot and Bouquet's equation, theory. Phrag- 



me'n, E. Stockh. Ofv. (1891) 623-. 

 theory of equations. Horn, J. Crelle 



J. Mth. 113 (1894) 50-. 



- F(U, ^)=0. Cayley, A. 



L. Mth. S. P. 18 (1886-87) 314-. 

 Calculus of symbols, with application to non- 

 linear differential equations. Russell, W. H. L. 



E. S. P. 13 (1864) 423-. 

 Class of equations. Picard, E. Bll. Sc. Mth. 



As. 4 (1880) (Ft. 1) 416-. 

 . Petrovitch, M. Palermo Cir. Mt. 



Ed. 14 (1900) 28-. 

 , 1st degree. Franklin, F. [1881] (xn) 



J. H. Un. Cir. [1] (1882) 165. 

 simultaneous equations. Guldberg, A. 



Christiania F. (1893) No. 18, 8 pp. 

 p-discriminant, and its connexion with general 



theory of envelopes. Chrystal, . Edinb. 



E. S. T. 38 (1897) 803-. 

 c- and ^-discriminants. Hill, M. J. M. [1888] 



L. Mth. S. P. 19 (1889) 561-. 

 Discriminants of algebraic differential equation, 



and its complete primitive. Torelli, G. 



A. Mt. 19 (1891-92) 254-. 

 Envelopes and singular solutions. Cockle, 



(Sir) J. [1877] Manch. Lt. Ph. S. P. 17 



(1878) 13-; 21 (1882) 98-. 



Equation of form f(u, j=0. Fuchs, L. 

 C. E. 93 (1881) 1063-. 



Equation of form -^ + Py m + Ry n = Q. Guld- 



berg, A. N. Mg. Ntvd. 31 (1890) 379-. 

 -- Jacobi. Mansion, P. Brux. Ac. Bll. 44 



(1877) 195-. 



-- 1st order and Jacobi's equation. Elliot, 

 . Par. EC. Norm. A. 7 (1890) 101-. 



in any number of variables. Pittarelli, G. 

 G. Mt. [13 (1875)] 323-. 



Equations, 1st degree. Darboux, G. C. E. 86 



(1878) 533-. 



with fixed branch-points. Wallenberg, G. 

 Z. Mth. Ps. 35 (1890) 193-, 257-, 321-. 



, general integral of which is uniform, class. 

 Picard, E. C. E. 117 (1893) 603-. 



, integral of which has form 



Painleve, P. Toul. Fac. Sc. A. 10 (1896) G, 

 37pp. 



, and singularities of their algebraic integrals. 

 Autonne, L. Par. EC. Pol. J. 2 (1897) 51-; 

 3 (1897) 1-. 



Eulerian factor and M + N ~- = 0. Hansen, 



P. C. V. [1873] Kjob. Dn. Vd. Selsk. Skr. 



10 (1875) 435-. 

 General integrable forms of equations, and their 



criteria. Mayer, A. Leip. Mth. Ps. B. 42 



(1890) 491-. 

 Homogeneous equations. Pullich, . (xn) 



Ts. Mth. 4 (1874) 39-. 

 -- . Frobenius, G. [1877] Crelle J. Mth. 



86 (1879) 1-. 

 -- , and Clairau't's equation. Mansion, P. 



Brux. Ac. Bll. 43 (1877) 169-. 

 -- , -- . Catalan, E. C. Brux. Ac. 



Bll. 43 (1877) 335-. 

 -- , --- . Folie, F. Brux. Ac. Bll. 43 



(1877) 506-. 



functions of n differentials. Lipschitz, R. 

 Crelle J. 70 (1869) 71- ; 72 (1870) 1-. 



Integrability. Peano, G. Tor. Ac. Sc. At. 21 



(1885) 677-. 

 Integrable forms. Bugaev, N. V. [1869] (xn) 



Eec. Mth. (Moscou) 4 (1869-70) (Pt. 1) 61-. 

 Integral of equation in 2 variables ; determina- 



tion of properties. Woisard, J. L. Gergonne 



A. Mth. 14 (1823-24) 97-. 



_ 



-- -p = + y/y* - cos 2x, property. Meissel, 



E. [1878] Arch. Mth. Ps. 65 (1880) 111. 

 Integrals, algebraic. PainlevS, P. C. E. 110 

 (1890) 945- ; 112 (1891) 1190-. 



, . Autonne, L. C. E. 113 (1891) 632-; 

 114 (1892) 407 



, , degree, limitation. Automie, L. C. E. 

 116 (1893) 132-, 1045- ; Par. EC. Pol. J. 63 

 (1893) 79- ; 64 (1894) 1-. 



of algebraic equations, limits of extension. 

 Lindelof, E. Par. S. Mth. Bll. 27 (1899) 

 205-. 



, behaviour near singular point. Horn, J. 

 Crelle J. Mth. 118 (1897) 257-; 119 (1898) 

 196-, 267-. 



389 



