272 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 



The symbolical form is 



/-D + 1 , ,,j jj-D + i , 3 . 



or 



or 



or 



or 



or 



, D 4- 3 '^ " 



, — -L) + « 





3 s^/_D + i y 



y-ae 



■2^d'l 



dx^- 



= 



X dxi 



,,=Av^5ri {2/^ '^^-^^^^} (Ex- 3, Class 2.) 

 dx \dxi dx^/ 



Ex. 10. 



The symbolical form of the equation is 



or 



,'^D + l , (n-iy .-—(l-D + i ./-IJ + n „_o 

 (l + aD)y-i^/^«'"-^^'^^(l + eD-|) .y=0 (1). 



This equation may be reduced in several instances : 



9 

 A. If c = 5 the equation becomes 



il + aD)2,-bV^le^"-'-^'-^jR^.;/ = 0, 



or 



or 



(1 



+ a-D)s,-Lv^ _E5±»_,("-i)^y=0 by (D.) 



D + w-l 



2 6 /— 1- 



3«' *(_D-i)/-D + «-t) 

 1. If- =l-«, equation (2) is reduced to 



l- B+'n ^^(»-»^^_n (2.) 



2 6 /-T- 

 y+3-y-l 



/-D+M-1 (n-ij« rt 



