PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. -267 



Ex.2. „_«;,§ ilZ=x. 



This gives y=^+ {\ + m a/^TI -~Ji±^ ) 



/-D + n-i ^ 



= +26r ( l + »? V -1 '— =^ 1 " 



CoE. If *=n, this expression must be reduced, as in Ex. 2, Class 2, to 



1 / /« + # X - 1 1 



fw + i V /•» / '^ 



• dn 1^ 



CoE. 2. As a particular case, the solution of 



d^ y 3 / ,- y f> ■ 



_ A 86 2, 



These equations might have been included in the preceding Class, to which, 

 both in their form and in the mode of their solution, they are very analogous. 

 They are, however, particular cases of Example 5, below, which does not belong 

 to that Class. 



Ex.3. ^ + „VJ?54 + S,^=0. 



The equation in 6 is (by C), 





Suppose y=2a„«~" ; then 



2a„ {l + .A/3T/^*-6^M..-"^=0by(A) 

 Hence any value of n which will satisfy the equation 



jn In 



will give a term in the solution. 



CoE. 1. If aV-l = - ;,-^, b = -r we havc 



