374 Dr. C. J. Hargreave on Differential 



whence 



dz=pdx + qdy=x* T ^ T *—X\ T \ dT \> 

 and 



18. By separation of symbols, the partial equation may be 

 written in the form 



(£+^ +R >iH(£ +( *'- R) 4H ; 



or in the same form with the sign of R changed. As the solu- 

 tion of this is 



which gives 



we observe that the solution of any equation of the form 



| + ( * l+ B)| + I^O 



is 



where c = r is the solution of -/ =6, +R. 



ax Tl 



The partial equation admits of some transformations ; among 

 which I may mention, that if we add to it an absolute term 



VfeVR dyJ~ t ~2dy\'R dp J/' 



the effect is to add to the value of z 



M(£)'^.£f+*.(f) , )->°rt 



with a similar function of f 2 . 



If we add to the partial the absolute term 



\i\ R w) + i\ n w)/ 



R 



the value of z is augmented by two functions of the form 



Mf^*>f;)-Mf+*-»>f)- 



