126 Dr. Hargreave on Differential 



we can solve 



— =zylru. 



yp 



For 



X V _->__WV T_f u -f u -i 



yp yp ■ u u 



Therefore the equation is solved by v—fu, where 



•^-^-1=^ or (fu)*=2$utyu+u)du. 

 Again, since 



y{px—y)-vyp-% r^jf^ —A 

 the solution of 



y(pos—y) = yjru 

 is v=fu, where 



r» udu 



Similarly 



{1+tft f' u ' 

 therefore — — , =i|rw is solved by v=-fu. where 



du 



J du 



More generally, since 



V±f)l<t>{x + yp)=fu<t>{fu) } 

 P 

 we have for the solution of 



( l J-P^ ^(x + yp)=yjru 

 P 



v—fu, where fu=(f>~ 1 (^r l u) ) the suffix denoting integration with 

 regard to u. 

 Similarly, 



£<l>(x+yp)-fu 

 is solved by v=fu, where fu = (j)~ 1 nuyjrudu). 



