4820 Ordinary Differential Equations, Solution and Reduction 4820 



of (A+A'x + A"y)(xdy-ydx) 



- (B + B'x + B"y) dy + (C + C'x + C"y) dx = 0. 

 Lebesgw, V. A. Liouv. J. Mth. 10 (1845) 

 316-. 



y"x Ax-y" + Bxy' + Cy), 

 y' = x* Ax' 2 y'^ + Bxi/ + Cy) , 



Spitzer, S. Arch. Mth. Ps. 42 (1864) 346. 



t method. Steen, A . 



Ts. Mt. Fys. 3 (1870) 24-. 



y"=x(xy'-ny). Spitzer, S. Arch. Mth. 

 Ps. 53 (1871) 117-. 



yW = Ax^y" + Bxy' + Cy. Spitzer, S. Arch. 

 Mth. Ps. 53 (1871) 385-. 



fix, y) dx + <(> (x, y) dy = Q, case. Harkema, 

 C. N. A. Mth. 13 (1874) 545-. 



(xdy - ydx) (a + bx + cy) - dy (a' + b'x + c'y) 



+ dx (a" + b"x + c"y) = 0. 

 Allegret, A. C. E. 83 (1876) 1171. 



- y g - | (g) 2 = 6/(x),/being a polynomial 



of 2nd degree. Laguerre, E. [18771 Par - S. 

 Mth. Bll. 6 (1878) 121-. 



Alexeeff, N. C. E. 87 (1878) 641-. 

 _/^ |t A = 0. Hansen, P. C. V. [1881] 



Kjob. Ov. (1881-82) 156- (& Resume, 7-). 



Ldx + Mdy + N (xdy - ydx) = 0. Hocevar, F. 

 Wien Ak. Sb. 85 (1882) (Ab. 2) 848-. 



-r-^ + p = P + fiip + /3 2 p 2 .... Lindstedt, A. 



As. Nr. 103 (1882) 257-; 104 (1883) 145-. 



= (Lindstedt). Gylden, J. A. H. 



As. Nr. 103 (1882) 321-. 



(A~&* + B~ 3 y* + Clx'y + Dp + E^y + F 3 \ f ~ ' 



(xdy -ydx)) 

 Heymann, W. Z. Mth. Ps. 28 (1883) 54-. 



<p (x, y, -p, ... T-^ ) > when it is an exact 



differential coefficient. Foldberg, P. T. N. 

 Ts. Mth. 1 (B) (1890) 23-; Fschr. Mth. 

 (1890) 281-. 



y"=Ay* + By 2 + Cy + D + (Ey + F) y'. Mittag- 

 Leffler, G.- Acta Mth. 18 (1894) 233-. 



Newton-Cotes method of quadratures. Jung, V. 

 Prag Ceske Ak. Fr. Jos. Ez. (Tfida 2) 8 (1899) 

 Art. 17, 12 pp. ; Fschr. Mth. (1899) 279. 



Non-linear equations, cases. Liouville, R. C. 

 B. 103 (1886) 457-. 



, class. Liouville, R. C. E. 103 



(1886) 520-, 571. 



, 2nd order, with doubly periodic co- 

 efficients. Gylden, H. C. E. 122 (1896) 

 160-, 585-. 



Partial equations occurring in theory of 

 conjugate functions. Volterra, V. Palermo 

 Cir. Mt. Ed. 3 (1889) 260-. 



Paths described by ships to perform certain 



evolutions. Bernotti, R. [1897] Ev. Mar. 



et Col. 137 (1898) 341-. 

 Eeciprocal equations. Orloff, . Brux. Ac. 



Bll. 33 (1872) 113-. 

 Eeduction to canonical form. Pennacchietti, . 



G. Mt. 29 (1891) 239-. 

 ---- . Riquier, C. Par. EC. Norm. A. 



14 (1897) 259-. 



of complete system to single system of 

 ordinary equations. Mayer, A. Leip. Mth. 

 Ps. B. 43 (1891) 448-. 



---------- . Schur, F. 



Leip. Mth. Ps. B. 44 (1892) 177-. 



order. Konigsberger, L. Mth. A. 26 

 (1886) 110-. 



--- by known integrals. Koenigsberger, L. 



Mth. A. 31 (1888) 302-. 

 to new variables. Baehr, G. F. W. Amst. 



Vs. Ak. 3 (1855) 233-. 

 Separation of variables in Mdx + Ndy = 0. 



Harkema, C. N. A. Mth. 16 (1877) 215-. 



115 



Solution. 



Roberts, S. QJ. Mth. 3 (1860) 218-. 

 asymptotic, cases. Picard, E. C. E. 

 (1892) 1030-. 



method, Petzval's. Spottiswoode, W. QJ. 

 Mth. 5 (1862) 154-. 



Boole's. Rawson, R. Mess. Mth. 5 (1876) 



138-. 

 cases. Bronwin, B. Ph. Mg. 32 (1848) 256-. 



(Bronwin). Boole, G. Ph. Mg. 32 (1848) 

 413-. 



. Williamson, B. Ph. Mg. 11 (1856) 364-. 



. Jackson, F. H. Edinb. Mth. S. P. 12 

 (1894) 109-. 



of class of difference or differential equations. 



Sylvester, J. J. Am. J. Mth. 4 (1881) 



260-. 

 common to two equations, orders m + n, m, 



Libri's theorem. Liouville, J. C. E. 8 



(1839) 790-. 



of differential resolvent. Russell, W. H. L. 

 Manch. Lt. Ph. S. Mm. 2 (1865) 



equation, 2nd order, properties. Routh, E. J. 

 L. Mth. S. P. 16 (1884-85) 245-. 



of sources. Hammond, J. Am. J. Mth. 



5 (1882) 218-. 



equations in series. Glaisher, J. W. L. 

 [1878] Mess. Mth. 8 (1879) 20-. 



homogeneous equation. Forsyth, A. R. 

 Mess. Mth. 18 (1889) 136-. 



and integration. West, E. Liouv. J. Mth. 7 

 (1881) 5-; 8 (1882) 19-, 125- ; 9 (1883) 301-. 



numerical. Runge, C. Mth. A. 46 (1895) 

 167- . 



periodic, of linear equations. Bendixson, I. 



Stockh. Ofv. (1896) 193-. 

 regular, of a system. Sauvage, L. Par. EC. 



Norm. A. 3 (1886) 391- ; 5 (1888) 9-; 6 



(1889) 157-. 

 singular. Fine, H. B. Am. J. Mth. 12 (1890) 



295-. 

 . Page, J. M. Am. J. Mth. 18 (1896) 95-. 



362 



