AEQVATIONFM DIFFERENTIALIFM. 2$ 



hinc ambae fun&iones P ct Q definiri poterunt \ re- 

 perietur enim : 



p ydV — nVdy ~. nVdx — xdV 



*■ ' — ydx — xdy ^ >C — " ydx — xdy • 



Coroll. 2. 



43. Quoties ergo V eft fun&io homogenea » 

 dimenfionum, toties ob ? — {---) et Q— (gj) erit 



/d_V> ydV—nVdy {tL) nVdx — x IV 



\dx) — ydx—xdy et \dy ) — y dx — xdy 



■vbi notandum eft , in his fractionibus differentialia fe 

 mutuo tollere , feu vtrumque numeratorcm fore per 

 ydx—xdy diuifibilem. 



Problema 6. 



44. Propofita aequatione difFercntiali Md x 

 •4-N^zro,in qua M et N fint funcliones homoge- 

 neae iplarum x et y eiusdem ambae dimenfionum nu- 

 tneri , inuenirc multiplicatorcm , qui eam aequationem 

 reddat integrabilem. 



Solutio. 



Sit n numerus dimenfionum , Ttrique fun&ioni 

 M et N conueniens, eritque per §. piaec. 



JM v n M dx-xdVk /4i?\ ■ ?** N — w jj d -> 



*dy ) — ydx — xdy ec Vd »)-— yd «— *dy 



ideoque 



Vdy)"""'d«/ —" y d x — * dy ~ • 



Iam ficile colligere licet, dari multiplicatorem, qui etiam 



fit funtfio homogenea ipfarum x et y. Sit ergo L talis 



Nou, Comm. Tom. VIII. D functio 



