4820 Ordinary Differential Equations, Solution and Reduction 4820 



General equations reducible to quadratures. 



Maximovitch, W. C. E. 101 (1885) 809-. 

 Greatest and least exponents in theory of dif- 



ferential equations, complete particular in- 



tegrals. Bugaev, N. V. [1891] Eec. Mth. 



(Moscou) 16 (1893) 39- ; Fschr. Mth. (1891) 



313. 

 Homogeneous equations. Lindelof, E. Par. S. 



Mth. Bll. 24 (1896) 35-. 

 Integrability conditions for linear equations. 



Eusjan, C. K. Fschr. Mth. (1899) 314-. 

 , formula, generalisation. Eestellini, L. 



G. Mt. 36 (1898) 262-. 

 Integrable case of 



+ (T + iv'kx) y' + w"ky = 0. 

 Thomae, C. J. Z. Mth. Ps. 21 (1876) 100-. 



cases of special equation. Heymann, W. 

 Crelle J. Mth. 113 (1894) 84-. 



class of differential and finite difference 

 equations. Sylvester, J. J. [1881] (xn) 

 J. H. Un. Cir. [1] (1882) 178. 



forms of linear equations, 2nd order. Liou- 

 ville, E. C. E. 100 (1885) 235-. 



total differential equations, theory. Guld- 

 berg, A. Crelle J. Mth. 122 (1900) 34-. 



Integrals. 



algebraic, of Lame's equation. Brioschi, F. 

 Em. E. Ac. Line. Ed. 1 (1892) (Sem. 2) 327-. 



particular. Bugaev, N. V. [1892-97] Eec. 

 Mth. (Moscou) 17 (1895) 399-; 19 (1897) 

 662-; Fschr. Mth. (1893-94) 538. 



cases. Herz, N. [1881] Arch. Mth. Ps. 67 



(1882) 312-. 

 of equation, 1st order, at singular point, values. 



Fuchs, L. Berl. Ak. Sb. (1886) 279-. 



equations, 1st order, with limited number 

 of values. Painleve, P. C. E. 114 (1892) 

 107-, 280-. 



-- with periodic coefficients, form. Anisimov, 



V. A. Eec. Mth. (Moscou) 20 (1899) 411- ; 



Fschr. Mth. (1898) 286-. 

 ----- , . Anisimov, V. [1900] Eec. 



Mth. (Moscou) 21 (1901) 62-. 

 ----- , . Hermite, C. [1900] Eec. 



Mth. (Moscou) 21 (1901) 66-. 

 expansions in series. Picard, E. C. E. 128 



(1899) 1363-. 

 --- , cases. Liouville, E. C. E. Ill (1890) 



597-. 

 first, of systems. Painleve, P. C. E. 124 



(1897) 136-. 

 as functions of their initial values. Niccoletti, 



0. Em. E. Ac. Line. Ed. 4 (1895) (Sem. 2) 316-. 

 ---- . Holmgren, E. Stockh. Ak. 



Hndl. Bh. 25 (1900) (Afd. 1) No. 4, 19 pp. 

 general, of Bessel's equation, formulse for nu- 



merical calculation. Niembller, F. Z. Mth. 



Ps. 25 (1880) 65-. 



, equation of 1st order, form. Fuchs, L. 

 Berl. Ak. Sb. (1884) 1171-. 



, certain systems of simultaneous dif- 

 ferential equations. Seiliger, D. Kazan Un. 

 Mm. (1897, Pt. 1) (Non-o/. Sect.) 69-. 



particular, with fractional indices. Bugaev, 

 N. V. [1891] St Pet. Ac. Sc. Mm. (Es.) 67 

 (1892) (Suppl.) No. 4, 12 pp. ; Fschr. Mth. 

 (1891) 313. 



and general, connexion between. Bochow, 

 Z. Mth. Ps. 33 (1888) 101-. 



of special equation, form. Haentzschel, E. 

 Crelle J. Mth. 112 (1893) 148-. 



system, calculation by Cauchy-Lipschitz 

 method. Painleve, . Par. S. Mth. Bll. 

 27 (1899) 149- 



of total differential equations. Sauvage, . 



Liouv. J. Mth. 10 (1884) 387-. 



systems. Forsyth, A. E. [1899] Camb. Ph. 

 S. T. 18 (1900) 35-. 



total differentials. Poincare, H. C. E. 99 

 (1884) 1145-. 



. Picard, E. C. E. 100 (1885) 843-. 



and class of algebraic surfaces . Picard , 



E. C. E. 99 (1884) 1147-. 

 uniform, of equations of 1st order and genus 



zero. Petrovitch, . C. E. 118 (1894) 



1190-. 



of 



: ~ z* + C. Wood, De V. Franklin I. 



J. 47 (1864) 28-. 



f(y, x, -^J = 0, representation in space. 

 Autonne, L. C. E. 105 (1887) 850-. 



Integrating equation. Bierens de Haan, D. 

 Amst. Ak. Vs. M. 14 (1879) 162-. 



factor. Buchwaldt, F. Mth. Ts. 5 (1863) 

 33-, 82-. 



, determination. Maksimovich, V. P. 

 Kazan S. Nt. (Ps.-Mth.) P. 2 (1884) 19-. 



-of elliptic equation. Sturm, E. Mth. A. 



21 (1883) 446-. 

 equations, 1st order. Winckler, A. 



Wien Ak. Sb. 99 (1891) (Ab. 2a) 457-, 875-. 

 expressions, 1st order. Collet, . 



C. E. 68 (1869) 799-. 

 , , for any number of variables. 



Collet, . Par. EC. Norm. A. 7 (1870) 59-. 

 homogeneous equations. Le Francois, 



(Prof.) . Brux. Ac. Bll. 13 (1846) 159-. 

 system of equations, new. Jacobi, 



C. G. J. Crelle J. 27 (1844) 199- ; 29 (1845) 



213-, 333-. 

 , theory. Dg. Ts. Mt. Fys. 2 (1869) 



127-. 

 ,3 variables. De Morgan, A. QJ. Mth. 



2 (1858) 323-. 



factors of one or several differential forms. 

 Chini, M. Mil. I. Lomb. Ed. 33 (1900) 601-. 



system of linear homogeneous equa- 

 tions. Escherich, G. von. Wien Ak. Sb. 

 101 (1892) (Ab. 2a) 1222-. 



Integration. 



Brassinne, E. Toul. Mm. Ac. 5 (1839) 139-. 

 Bertrand, J. Liouv. J. Mth. 17 (1852) 175-. 

 HiU, C. J. D. Sk. Nf . F. 8 (1860) 525-. 

 Steen, A. Ts. Mt. Fys. 3 (1870) 44-. 

 Spitzer, S. Z. Mth. Ps. 52 (1871) 1-, 16 ; 53 

 (1871) 1-. 



359 



