366 Dr. C. J. Hargreave on Differential 



and the complete primitive is 



c 2 — 2c%x-\- (x x ) <2 ~ x l°g x-\-y + x = 0. 

 Ex.4. Let cj> l = {l-j-x 3 )y, a = y a (l— 20 s + 4a?*logy); then 

 P= , and -57= -^-x 2 . The system then gives 



X A 



and the complete primitive is 



c 2 — cx 2 -\- logy— x = (Boole, p. 184). 



Ex. 5. Let £,=!^, <t>2=V 2 hgy, R 2 = ^(a 2 -41ogy); then 



-r-= — i — p-^, and -33- = log logy. The system gives 



whence 



^ S V v / log7 \logy //' 



and the primitive becomes, after reduction, 



c l -cx+ log j/=0 (Boole, p. 162). . 



fe.6. Let>,= J <p 2 =e«, B*=«"(^_A). then 



| = i and w = logy. 

 The system gives 



dy~y\ e 2 V ' dx \ e 2x / ' 



whence 



and the primitive is 



cy-2ce* + l = 0. 



Ex.7. Let^=^-^ 2 =p4^ ; 



The system gives 



— = -, and-s7 = logy. 

 92 2/ 



g = f (1-^rt £--*0-*r^ 



