AEQVATIONVM DIFFERENTIAUVM. +$ 



-vbi R fit fundio quaecunque ipfius x, fumto difTeren- 

 tiali dx conftante. Iam quaero funclionem ipfius x, 

 per quam ifta aequatio mulriplicata euadat integrabilis. 

 Sit S ifta functio , et aequationis 



Sd*L-\-4.SRdLdx 2 -\-2.SLdRdx* — o 

 integrale erit "" 



S^L-^S^/L-hL(^S-f-4SR^)r=:2C^ 

 idummodo fit 



J* S -+- 2 S dK dx 2 -f- 4R dS dx 2 zz o. 

 Sufficit fcilicet quemuis valorem particulariter fatisfacien- 

 tem fumfiffe. At haec aequatio, per S multiplicata, ne- 

 gleda conftante, dat integrale : 



SddS-\dS*-\-zSSRdx 2 zz:Q. 

 Ponatur Szr^ 3 ^^*, eritque 



zdv-\-±vvdx-\- nRdxzzo 

 \nde negotium huc redit , vt pro v faltem valor par- 

 ticularis inueftigetur , qui fatisfaciat huic aequationi diffe- 

 rentiali primi gradus: dv -\-vvdx-\-Rdx~o , qnem 

 igitur tanquam conceffum afiumo. Hinc noftra aequa- 

 tio femel integrata erit, ob S — e 2 f vdx , 



ddL- zvdxdL+Liidvdx+^vvdx^+Rdx^zCe—^^dx 2 

 Cum igitur,ob Rdxzz:— dv— vvdx, habeamus 



ddL-zvdxdL-zLdxdv— zCe- 2lvdx dx] 

 eius integrale manifefto eft : 



dL - zLvdxzz. B dx~\~ a CdxJ e~ 2 ^ vdx dx 

 ct per f"^" 1 *, denuo multiphcando integrale, prodibit 



c-* vd *L=zh+BJe-> vdx dx\-2Cfe-^dx/e- iSvdx dx 



F 2 Quare 



