lK = f »** » = lp-~ll(mp*-hn), 



J mp^ + ^-hn p r 



i — x 



ldeoque K r_ - r hincque II r_ — ! — l. 1 y mi . 



(mp^-^-nf PP 



dc formula integrabilis erit 



I--X 



(mp K ~ + ' 1 x-i- n y) (mp x ~ {-n) x dp 



p p 



i 



quippe cums lntegrale ent _- =L_i l i. 



P 



Problema 3. 

 Invenire duas fun&iones ipfius p, quae fint P et Q 5 

 ut ifta formula differentialis : (p x — y) n — l ( P x 4- Q/) p 

 ,/zar. integrabilis* 



Solutio. 

 $. 3*. Cum fit tfdprz: a. (p<c — y), erit 

 fPxdp^px-yf- 1 — l n V(px-yY-lf(px-yY?)V. 

 Deinde cum fit ^_a.(x-i), loco Qy d p fcribamus 

 Qpp.yAP, tum vero ]oco px—y fcribamus p(x— £),ideo- 

 que loco (p x — yf" 1 fcribendum erit p n — * ( x — ty- x . 

 Hinc ergo pro altera parte habebimus 



<lyd p (px-yf- 1 — Qpp . lAP . p*-* ( x _ ry-* 



3= Q. p 71 "t J . 2-* . ( x — y f - * 



hincque per reduaionem erit 



P * /Q 



