PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 261 
see the reason of this analogy. We shall, in Example 7, exhibit a complete and 
general solution of all equations of this form. 



















dé 
Ex. 6. —m x? —2 =0 
A B C A B 
= 2 1 1 1 ae ae 
Let y=Axv?+Ba+C+ eh eS gamers ae 
pes ao Be + &e. 
av Ue 
then Aa? +Bo+C+ 1 4 &e, <mV=1 (Eo? A, +&e.) 
Aw Aes |B A, |B 
1. —— =, A, = t —,A,= 2__ '— &e. 
Payette St my =! 6 . 
B B [4 B. jee 
pe EN eer eel Np es ed I 
emf —Tj2° 2 mf fg? mV I fF ; 
Cals C iall8 C, [| 
2 Gia ee Gy, ee gn, 
BPS 6 wears ° my 1 8 
This gives us six separate series. 
f AC ah 2 1.2 1.2.6.7 
te Ad + wt gtte=AW—sz a) a wy) eee 
G2 yak ee 1.2 
Let ater Tne Bae eas, 
AEE 12 
ee 1 345.3 me eee. yt 
ii ile piineiatesead wit Lj 2 Und 
das 3.4 mat 4.3.$mtat 
gl05 ee tA ay 
= 32 m x= a 2" 
d*y, 3 d*y, 3 dy, 3 105 era y 
or Ce Pee ee da So, BF es aot 
dy, 3 La, 3 dy 3 105 
Br ee ae S270 ace ae 
A A Ris 1 te eee 17 eesa9 
ait +k, gives — a({-5 7S eet: : 
e's, 7-1 sik Age igias ° 5.4.5.8.9.100P oF 
Bey. eh Z.3 
re al Vik Sema aS 
VOL. XVI. PART III. 7 Lit 
