PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. £55 



y=(l — ^/3T/^)-^0. 

 Suppose y=2a„e~'"'; then 



2a„(.'-'-»»^/^te.-"^) =Oby 



(A) 



which can be satisfied only by making i_»8 -/-i L + ^ =0 ; giving, consequently, 



In 

 only one value of « ; 



Hence y= — is the complete solution. 



Cor. If 



n=l and i/= — . 

 Ex.2. y-nWlc^=X. 



The equation in 6 is ^-mV-l'-^=^y='P «-' 



= A +2 6 /i_,„V^/!:±i\ -\-r^ (Ex. 1 and A) 



x" \ 'r I 



CoR. If r=n; this expression becomes infinite. We must,- in this case, wi'ite 

 » + c in place of r, expand in terms of c, and finally put c=0. 



We have, thus, ^^ '■ 



1 „. . / — T l^ + h 1 . / — T /In+i d In + i , . ■\ 



1 — m V — 1 ' — ~ l — mV—l I ' _ + -^ ' — ^ . c + &c. I 



/r V. fn an jn I 



+ &C. 



-, / — i-w + i / — -z d In + i 



l — mv —I '— =-^ cmv —1 3— ' ^ 



/» «» /n 



-ndg 



1 / — r/'i + i / — T d In + k 



1 — ?«V— 1 — =^ »?v— 1 :r-'— ^ 



