274 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 
Now, on examination, it appears that the proposed equation is nothing more 
: : 6 : 
than the differential coefficient of the quantity em y—z=0 added to n times 
x 
the quantity itself: Thus, 
d (dty diy a 
4 (Sons) sn(Zfomrer) 



gives 
dy doy. dm dz d>y 
es MO Oe — Ge thy tmny—nz=0 
or FD ON eae Cae (“2 +m n— = 
dx: dx dat PI~ de dx p)u=a 
; d d 
provided 7. tne=g and 7 tmn—p=0. 
Thus it appears that the equation is not solved but formed: and this is pro- 
bably all M. Besce intends. How he can justify his additional remark, that 
d* y 
d x? 
able to conjecture. 
———+my=z can be solved if m is a constant, or a linear function of 2, I am un- 
Ciass 4. Equations which are capable of solution by the division of operations. 
17. We have already met with several equations in Class 1, where the total 
operation was found to be equivalent to the product of two or more partial opera- 
tions; and in Art. 9 we have pointed out the manner in which the partial opera- 
tions are applied, viz., by decomposing the total operation in exactly the same way 
as an ordinary fraction is decomposed into partial fractions. 
ES 
4 
ze a a 0. 
Bx ai. Dee * 74 

This equation, when reduced to the symbolical form, is 
a 
+ 
—_ 
i ii os 








Oty eae es 
y+ae pete PIE Ditth ep tile [alts 09 
|-D ie 
a Th oe PS 
eps EBED. dy te (SEE). domo 
Now pH es egg | aE ee 
/—D+1 /-D+% /—D+2 /—D+1 
/—-D+2 ye /-D+14/-D+1 @ 
— —3 = .e?y by (D 
(S55 Abe =Dae /2Da4 ey by (D) 

