PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 263 



C, , Gs SmG, oe. =) aBow,oF dd 
e : a dk (Ao, Se =— — ae = See) 
4 xt ES avai (ae 2.5.6.7 ma? 
_vro #y, 
m/f —1 dz? 

ie ed 
ae rea the same as y, ; 




Sa ca vm dy, PY 4 vm wy, 
and y=4 (75 Ne Ek a) +B (Se + im Jat — 
Py, Num _ ay, 
ie (ae on i ae) 
It is scarcely necessary to point out the analogy which exists between the 
differential equations which determine the value of the transcendentals in this 
and in the preceding examples. 
14. We proceed now to exhibit a general solution of equations of this kind. 
pad) =0; » beng any integer. 

Bx,.-/. ae psc 
The symbolical form of this equation is 
a ee Rb d> 
2 {naedt (Tata dk x” db 
(1) 

d 
=(1+ m2” d*)v=v+m2x" 
dx} 
where v is determined by the equation 

1 
(a ee es 
$ dk wv 
Le pao pir ame © (gn 5 —0 9 
v—m x” d? x” d? 7 = 0 Or v ma © (ano) (2) 
Tins dt» _ d®-*z 
Let = ————_ + pee 
th ee then da”—4 
2 (72) ee 1 won ge—ly 
dat dat da 2 a x1 


(Part I. Art. 11.) 
