266 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 



d.r" ^ C?r"-1 



.-. the equation for determining v is 



d"z (r + i) « (/"-I z (/• + i)(r-^) n(n-l') d"-'^ z . 



^2.,2n ^^n_(2r + l) ^2;r2»^ ■ ■ ■ ■ K ) 



w is the particular value of w corresponding with X=0. Having thus obtained v 

 and w, equation (1) gives the complete value oiy. It must be observed, that the 

 transformation from v to z is only to be made when n is greater than 2 ?• + 1 . 



Class III. UqiMtions which are capable of solution by transformation, without 



division of operations. 



15. Ex. 1. y-mx^ -^^0 



d x^ 



By (C) this equation is transformed into 



y-m\-lf'^=^y=Q, or 



Hence, as in Ex. 1, Class 2, the value of y is y=— , where n is determined 



by the equation 1 + W^ ^^^i-^=0. 



4 _ _ _ 



CfiE. If m=- g^- ^— ^ , />» + f=i . iV'rrin = ii[n 



n~l; and !/=— . 

 z 



