AEQVJIIONVM DIFFERENTIALIVM. 6t 



rum dkiidatur , quoties conftanti arbitrariae aequatus 

 dabit integrale completum. Quare aequatio ydy+^~~ 

 — f—r t zz o generaliter integrata praebet : 

 (j + M) B+ ' ((» +- t)jr-*M) & Conft. 



Problema i5. 



9<J. Propofita aequatione ydy+Vydx-\-QdX-O v 

 inuenire conditiones funclionum P et Q > vt huiusmodi 

 multiplieator (yy-i-My-t- N)* eam reddat integrabi- 

 lem. 



Solutio. 



Ex natura dinerentialium fit necefle eft : 



r~ x <r-y(yy+My+N) n =: $- y d. (Pjr+Q> (yy + M/+ Nf 

 Cum lgitur M , N T P et Q, fint per hypothefin fun,- 

 ftione* ipfius #, erit, facta euolutione : 



*j(^+"Mj/-+N) B -- r (^+-^) = P(j/+M^+Nf 

 +- n ( P/+-Q) ( 3J+- M ) (yy +- Mj +- N)*~ f 

 et poft diuifibnem per (xr +-Mj'+-N) n— * 



«m*+-l* -(**+- 1 )PjTHr ( »-*-r )PMjr+-PN 



-+-2aQy -4-»QAt 



Hinc fiere oportet : 



I. ndM — (zn-}--i)?cfx 



IL «</N=z(«-{-i)PM</x+-2»Q/^ 



III. o — PN+-»QjVl 



Prima dat P~ ( t^W» et v&im3 Q.— ^t 



Ii 3 £u 



