PROFESSOR KELLAND OX GENERAL DIFFERENTIATION. 25£» 



and that the result of substitution is 



■li /2 Va: 11 



x^ X x^ ' ^ \/| "^ ,3 ^§ /-I a;' y 

 SO that 



g_/l A__ . (^^/2 B__^ /i /2 1 



/I m\/-\' ji mV-1 ;1 ;| »'^ 



/4 »i-v/_l 1 /| /4 w,V-l 



/I li /4 /y w^ 

 and also 



o_/l .^i_ -,_ ;§ ,3 a ._ ,f 3 li a 



/2 jwV'-l' 12 li m^' /2 /J /5 mW -1 



/2 /I /5 /V »»' 



_,r 1 1.4 1.4.7 



^ t'^ i.im^x^'^i.^.i.im^x^ ^. I .1 .| . y . y w"^""'" *''• 



?«v — 



-^ / 1 t , I • y I • V ■ V \ 1 



"HTWa; 2.3»8=x^ 2.3.5.6ra*a'Si 2 . 3 . 5 . 6 . 8 . 9 /«» ^"^"^ ^''•j J 



(,_ 2 2.5 2.5.8 



'^J-*- a .'5*m2«3~'"3 5 9 11*«4«.6 3 B S 11 Ifi 17 R„o + ^C* 



+ 



f . I m^ x^ I . I . I . V m" X' i . i . -I . y . y . y m" x^ 

 ^^/-iVa'? S.4:m^x°^ 3 . 4.6 . Twj^a'V '/) 



Each of these four series is the integral of a differential equation of the se- 

 cond order. 



Let J = •^ -1 — i — 2— 2 + T — i — r-,— r «- &c- 



and ^V^^5 3 ^^ 1 1 



rfa?'^ 2 ' 2 2 »i^a?"' ^ . I »j4 37 V 



_15 _1_ dy^ 



~8 ^""^^^^^rf^ 



+ &c. 



or ^+/1 ?_\'^_Ji,=15 



dx' \x m^ x'') dx 4x^ 8 



