2.66 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 


ae ee ed) Siakomsts q27—n+1 Ps 
s a pe re 
d d®-l x 
—s nu Je + 1 n—1 2 
ax” G a)ne ie 
aoe oe (r— ante Ae oie 
qr-@ r+1) Zz 
.. the equation for eer v is 
(r+3)n ad sit , CES) n(m—1) d™-? 
— 2 Wi nudatcr 1.2 ae dx" gt Ge. 


aes (r—4)....(r—2 +8) 
SOs Pane n 
-n(#—1)...1L.2 
1 d™-@rtl) » il 
hee” CP Cres | ee BET NE Tp FON) 
w is the particular value of v corresponding with X=0. Having thus obtained 
and w, equation (1) gives the complete value of y. It must be observed, that the 
transformation from v to z is only to be made when » is greater than 27+ 1. 
Crass III. Equations which are capable of solution by transformation, without 
chvision of operations. 

15. Ex. 1. y—mx? ay ==) 
By (C) this equation is transformed into 

y—m(—1)? — Pty =() or 
ae 
y= (14 m/—1 + SEE 10, 
: ; A : 5 
Hence, as in Ex. 1, Class 2, the value of y is Y= where 7 is determined 
jn+3 
|n 
by the equation 1+ m/ 1 “+2 —o, 

