PROFESSOR KELLAND ON GENERAL DIFFERENTIATION, 


di oe: (F5- ax) qv-1 le n(n —1) q-2 4 



Dw m2 v2 % dat-1 2.4 a Get Se 
Sit yy St eS) = 
AWA hee! m(n—1)....1 
eu) ST Ske Ra a cae 
Cor. 1. If n=1, the equation for determining w is 
ies, ( 1 1 xX 
dx erase 0S ne 
ees - 
: i “ e ma mn X 
of which the solution is “= ———_— ee Ee 
AED m= wt 
Ms Ae mz 
WE a 
: il aE 1 
Mm? 22 mx 
and y= (1+mx <5) ee 2 oe ee ae 
Cor. 2. Ifn=1, X= = it is evident that 
u= 
Jax ae aaa 
6 : b mbV/—1 
Ris 
where y, is the solution of the equation without X (Ex. 3.) 
265 
It appears, therefore, that the complete solution of equations of this form is 
reduced to the solution of ordinary linear equations, and the determination of the 
half differential coefficient of the results. 

Ex. 9. y—mnx 
nm gr+ & 
aethave X+0 limad 

Pm at PE me a aE a att 
where v+w is the solution of the equation 
‘ (1m? 2" drt a q’+t 
CeO) 
(1) 
Now qd’ t+% n dren nN gGrtly 
Captian pe BOT Ree, DENG 7 n+ 
darth” dattt =e dz2ttl a (7+ 3) nx 
(r+4) (7-4) ayaa 8 
+ 1.9 n(m—1) x eal = 
VOL. XVI. PART III. 
&e. 
oD, 
jd" » 
daz” 
5 =x, where » and r are any whole numbers. 
x . 
