4820 Ordinary Differential Equations, Solution and Reduction 4820 



singular, of algebraic equations, 1st order. 



Hamburger, M. Crelle J. Mth. 112 (1893) 



205-. ' 

 , equations, 1st order. Darboux, G. Bll. 



Sc. Mth. As. 4 (1873) 158-. 

 , , . Kapteyn, W. Bll. Sc. Mth. 



12 (1888) 135-. 

 , , . Predella, L. G. Mt. 33 



(1895) 31-, 183-. 



, , . Maddism, I. QJ. Mth. 28 



(1896) 311-. 



, , . Toussaint, H. Em. N. Line. 



Mm. 13 (1897) 283-. 

 , , . Petrovitch, M. Mth. A. 50 



(1898) 103-. 

 , , higher order. Hamburger, M. Crelle 



J. Mth. 121 (1900) 265-. 

 , homogeneous equations. Johnson, W. W. 



Mess. Mth. 16 (1887) 186-. 

 , integrable equations, 1st order. Work- 

 man, W. P. QJ. Mth. 22 (1887) 175-, 



308-. 

 , simultaneous equations. Goursat, E. 



Am. J. Mth. 11 (1889) 329-. 

 , and theory of congruencies. 



Dixon, A. C. [1894] Phil. Trans. (A) 186 



(1896) 523-. 

 , a system. Biermann, O. Wien Ak. Sb. 



90 (1885) (Ab. 2) 897-. 

 , of equations with n dependent 



variables. Hamburger, M. Crelle J. Mth. 



122 (1900) 322-. 



symbolic and by definite integrals of -~=x m y. 



Fields, J. G. Am. J. Mth. 8 (1886) 367-. 

 dy 



of ~=f(x, y) without Cauchy-Lipschitz con- 

 dition. Osgood, W. F. Mh. Mth. Ps. 9 

 331-. 



Substitution of variables as method of finding 

 integrating factor. Ermakov, V. P. (xn) 

 Kharkov Mth. S. Com. (1881) 3-. 



Successive approximations. Picard, E. C. E. 

 115 (1892) 543-. 



. Bendlxson, I. Stockh. Ofv. (1893) 

 599-. 



. Lindelof, E. Liouv. J. Mth. 10 (1893) 



. Picard, E. Liouv. J. Mth. 9 (1893) 



217-. 

 . Bugaev, N. F. [1896] Eec. Mth. 



(Moscou) 19 (1897) 1-; Fschr. Mth. (1896) 



70, 72. 

 . Picard, E. Am. J. Mth. 20 (1898) 



87-. 

 . Davidoglou, A. C. B. 130 (1900) 692-, 



1241-. 



, application to equations, 1st order. 

 Lindelof, E. C. B. 118 (1894) 454-. 



, , . Picard, E. C. B. 118 



(1894) 457-. 

 , , . Horn, J. Mth. A. 51 



(1899) 346-. 



divergent approximations. Picard, E. C. 

 B. 118 (1894) 899-. 



Symbolic decomposition. Cockle, Jos. Ph. 



Mg. 24 (1862) 288-. 

 System of equations, determination of variables 



satisfying. Cauchy, A. L. C. B. 23 (1846) 



485-, 529-. 

 Systems of equations. Combescure, E. [1874] 



Crelle J. Mth. 80 (1875) 33-. 

 --- . Halphen, G. H. C. E. 92 (1881) 



1404-. 

 --- . Guldberg, A. C. B. 117 (1893) 



215-. 

 --- , C ase. Halphen, G. H. C. B. 92 



(1881) 1101-. 

 --- , . Brioschi, F. C. B. 92 (1881) 



1389-. 

 --- , 1st order, having fundamental sys- 



tems of integrals. Vessiot, E. Toul. Fac. 



Sc. A. 8 (1894) B, 33 pp. 

 --- , 2nd order, in involution. Goursat, 



E. Par. EC. Pol. J. 3 (1897) 75-. 



, integration of which is reducible to that of 

 total differentials. Riquier, . C. E. 127 

 (1898) 809-, 1194-. 



Theorem of mean, extension to equations, 1st 

 order. Petrovitch, M. C. B. 128 (1899) 

 981-. 



Poincare on systems of 1st order. 

 Bendixson, . C. B, 118 (1894) 971-. 



Total algebraic differentials. Picard's equation 

 Pdx + Qdy = when F (x, y , z) = 0. Noether, 

 M. Mth. A. 29 (1887) 339-. 



Transformation, case. Hargreave, (7. J. Ph. 

 Mg. 30 (1847) 8-. 



of equations, 1st order, case. Painleve, P. 

 C. E. 110 (1890) 840-. 



--- with 2 variables. Zeuthen, H. G. 

 N. Ts. Mth. 1 (B) (1890) 1- ; Fschr. Mth. 

 (1890) 316. 



and integration of differential systems. 

 Delassus, E. Par. EC. Norm. A. 14 (1897) 

 195-. 



: --- simultaneous equations, several 

 variables. Brassinne, E. Toul. Mm. Ac. 5 

 (1839) 129- ; Liouv. J. Mth. 10 (1845) 194-. 



of linear equations, 2nd order. Spottiswoode, 

 W. Tortolini A. 3 (1852) 26-. 



--- , , with linear coefficients. 

 Bolza, O. Am. J. Mth. 15 (1893) 264-. 



-- ^2 + ^ + *& + 03 = - Heymann, 



W. Z. Mth. Ps. 27 (1882) 374-. 

 Transformations. Bianchi, G. Tortolini A. 3 



(1852) 347-. 

 Variation of arbitrary constants. Liouville, J. 



Liouv. J. Mth. 3 (1838) 342-. 

 -- constants in solutions. Brunacci, V. 



Turin Mm. Ac. (1804-05) (pte. 2) 3-. 



Sturm, J. C. F. 



(gr-l)V 

 L'l. 1 (1833) 247-. 



y" + f (*) y' + F (y) y'- = o. Liouville, J. 



Liouv. J. Mth. 7 (1842) 134-. 

 ^| + / (x) sin y + F (x) cos y + <f> (x) = 0. Besge, 

 V. A. Liouv. J. Mth. 11 (1846) 445. 



363 



