4880 Non-linear Differential Equations of Higher Orders 4880 



Equation connected with y n - ny + (n-l) x = 0. 

 Cayley, A. [1862-66] Manch. Lt. Ph. S. 

 (1865) 111-; Ph. Mg. 32 (1866) 



singular, theory. Cayley, A. Mess. Mth. 6 



(1877) 23-. 

 , . Hollman, P. J. N. Arch. Wisk. 



7 (*1881) 59-, 150-. 

 special. Vasil'ev, A. V. (XH) Kazan Un. 



Mm. [14] (1878) 309-. 



Systems of equations. Escherich, G. von. 



Wien Ak. Sb. 108 (1899) (Ab. 2o) 621-. 

 Theorem. Eadau, E. C. B. 66 (1868) 904-. 



of Darboux, on equation 



P (x, y , z) dx + Q (x, y, z) dy = 0. 



Picard, E. C. E. 100 (1885) 618-. 

 Theory. De Morgan, A. [1854] (rx) Camb. 



Ph. S. P. 1 (1866) 136-. 

 . Bertrand, J. C. E. 45 (1857) 617-. 



of equations, 1st degree. Autonne, L. Par. 

 EC. Pol. J. 61 (1891) 35-; 62 (1892) 47-. 



, general. Peano, G. Tor. Ac. Sc. At. 33 



(1897) 9-. 

 , paradox in. Tanner, H. W. L. Mess. Mth. 



10 (1881) 158-. 

 Transcendental integrals of equations with 



coefficients of 2nd degree. Winckler, A. 

 Wien Ak. Sb. 84 (1882) (Ab. 2) 



Transcendents. Konigsberger, L. Acta Mth. 



3 (1883) 1-. 

 Transformation. Russell, W. H. L. Camb. 



and Dubl. Mth. J. 9 (1854) 81-. 

 . Zorawski, K. Krk. Ak. (Mt.-Prz.) Ez. 



6 (1893) 67-; Crc. Ac. Sc. Bll. (1892) 



292-. 



=/ (u, z), proof of theorem of Cauchy. 



Ascoli, G. [1871] A. Mt. 5 (1871-73) 14-. 

 *<l> (y') + yt (y') + X(V') = O- Heymann, W. [1878] 

 Z. Mth. Ps. 24 (1879) 252-. 



-& . Sonin, N. Ja. [1894] St Pet. 

 Ac. Sc. Bll. 2 (1895) 93-; 3 (1895) 339-. 



dx 



4880 General theory of ordinary 

 equations, not linear, of order 

 higher than first. 



Fais, A. G. 



G. B. 



Abridged form of equations 



Mt. 12 (1874) 320-. 

 Addition theorem. Mittag-Lejfler, 



A. Ep. (1894) 561. 

 Algebra and group theory of equations. Loewy, 



A. Mh. Mth. Ps. 8 (1897) 225-. 

 Class of equations. Picard, E. C. B. 104 



(1887) 41-. 

 including those of all geodesies. Liou- 



ville, R. C. E. 105 (1887) 1062-. 

 Construction of equations of form 

 1 cPz 

 ;dxTy = X ^> 



admitting an explicit general integral. Mmt- 



tard, T. Par. EC. Pol. J. Cah. 45 (1878) 



Equation of algebraic curve. Chrystal, G. 

 Edinb. Mth. S. P. 3 (1885) 95-. 



Mm. 2 

 379-. 



, 2nd order. Enneper, A. Z. Mth. Ps. 15 

 (1870) 56-. 



, nth order, 2 variables, conditions for deri- 

 vation from equation of (n - l)th order. 

 Raabe, J. L. Crelle J. 31 (1846) 181-. 



Equations, general integral of which is uni- 

 form. Painleve, P. Par. S. Mth. Bll. 28 

 (1900) 201-. 



, , class. Picard, E. 



C. E. 110 (1890) 877-. 



, 2 general, of 2nd order, 7ith degree, derived 

 from the known linear equation. Rawson, 

 R. Mess. Mth. 2 (1873) 185-. 



integrable by meromorphic doubly periodic 

 functions. Petrovitch, M. Acta Mth. 22 

 (1899) 379-. 



, integral of which has finite number of 

 determining values. Painleve, P. C. E. 

 116 (1893) 88-, 173-. 



in lunar theory, two. Cayley, A. [1871] As. 

 S. M. Not. 32 (1872) 31-, 201-. 



, 2nd order. Vessiot, E. Toul. Fac. Sc. 



A. 9 (1895) F, 26 pp. 

 , , class. Wallenberg, G. Crelle J. 



Mth. 120 (1899) 113-. 

 , , with fixed critical point and uniform 



correspondence of surfaces. Painleve", P. 



C. E. 117 (1893) 611-. 

 , and 3rd orders, normal form. Pick, G. 



Mth. A. 38 (1891) 139-. 

 , 3rd order, case. Brioschi, F. E. S. P. 27 



(1878) 126-. 

 , , Schwarzian derivative. Klein, C. F. 



Leip. Mth. Ps. B. 35 (1883) 1-. 



possessing fundamental first integrals. 

 Guldberg, A. Christiania F. (1894) No. 1, 

 41 pp. ; Fschr. Mth. (1893-94) 544-. 



Homogeneous equations, 2nd order. Steen, A. 



(xn) Ts. Mth. 1 (1883) 11-. 

 , . Appell, P. Toul. Fac. Sc. A. 



3 (1889) K, 12 pp. 

 , . Wall 



Wallenberg, G. Crelle J. Mth. 



119 (1898) 87-. 



Integrability. Bach, , & Stoffel, . Liouv. 

 J. Mth. 7 (1862) 49-. 



, conditions in quadratures of equation of 

 2nd order. Yur'ev, S. A. [1869] (xn) 

 Eec. Mth. (Moscou) 4 (186970) (Pt. 1) 246-. 



Integrals, asymptotic representation for large 

 real values of argument. Kneser, A. Crelle 

 J. Mth. 116 (1896) 178-; 117 (1897) 72-; 



120 (1899) 267-. 



common to 2 systems. Capelli, A. Nap. 

 Ed. 39 (1900) 100-. 



several systems. Pennacchietti, G. 

 Catania Ac. Gioen. At. 3 (1891) 1-. 



, form near critical points. Picard, E. 



C. E. 87 (1878) 430-, 743-. 

 , singular. Zajaczkowski, W. [1873] (xn) 



Krk. Ak. (Mt.-Prz.) Pam. 1 (1874) 45-. 

 Integrating factor of equations of form 



A + By' + Cy' m + Dy' m + l + Ey' m ~ l y" = 0. 



Andreevskii, M. A. (xn) Eec. Mth. (Moscou) 



4 (1869-70) (Pt. 1) 143-. 



392 



