PROFESSOR KELLAND ON GENERAL DIFFERENTIATIOX. 



and the equation is reduced to 



275 



./ /-T/ -D + 1 f o -D + 1 il-B + l ' 



l-B + i /-D + A i~B + i ^ 



Let us abbreviate the operation ,_ ^ e^^ by c^, and the equation becomes 



If 1 + J -\/^ z—2az-—(l + as)(l + ^g); this equation is equivalent to 



{l + a(P){l + l3(P)y = 



or 



.0 



0- 



(l + a^)(l + /3^) ■ a-/3']+a(^ a-^l+/3<^ 



Now 



, , /-D + 1 - " /-D + ^ 



-D 



l-D + i 



= 1 — a V -1 a; — - 



Hence the solution of the given equation is reduced to the solution of the 

 two equations 



or 



Now these equations have been solved in Class 2, Ex. 3, and they give 



1 1 



Be''"-'' { 1 r e ''"■'■ V'^1 



and 



y= 



0= 



0- 



/3 



. 



(1- a </))(! -(8 (^) ■ "~a-^l-a(^ ■ a-^X-^tp 



_!_ 1 



It will be readily seen that B is not an arbitrary constant, independent of A. 



