32 DE INTEGRATIOKE 



Problema 9, 



56. Propofita hac aequatione differentiali : 



dy -+- Fydx -+- Qyydx -+-Kdxzzo 

 vbi P , Q et R fint fun&iones ipfius x tantum , fi 

 conftet, huic aequationi fatisfacere yzzzv , exiftente 

 fundhone ipfius x , inuenire multiplicatores , qui iftam 

 aequationem reddant integrabilem. 



Solutio. 



Cum aequationi fatisfaciat valor y ~v , erit 

 dv-h^vdx-i-Qyvdx-h-Rdx—Q ^ 

 li ergo ponatur yzzv-\-\ , faabebitur 



fiue : 



dz— (?-\-zQy)zdx— Qjxzp o 

 quae integrabilis redditur pei multiplicatorem 



Hic ergo multiplicator per zz multiplicarus conuenict 

 aequationi propofitae. Cum ergo fit srrj^— ;, multi- 

 pliator aequationem propofitam integrabikm reddens 

 erit : 



1 p<— /{F-fr-aQju^d* 



Sit breuitaf's gratia ^— /< p -*- s( i-*>> d *_rS. Quia aequationis 

 dz— (P-H 2.Qy)zdx-Qdxzzo integrale eft 



Sz—fQSdxzz Conft. 

 omnes muitiplicatores quaefiti continebuntur in hac forma: 



vty 



