34- DE INTECRATIONE 



Coroll. 4. 



60. Quodfi ergo haec formula dy ^*i y y+M$+vr ~ 

 fuerit integrabilis , denominator ita debet effe compara- 

 tus, vt fit 



SL=:A-BV-i-CVV,SM_:S(B-2CV) 



-ftw(A-BV-i-CVV) 

 et SN~CSS-S*?(B-2CV)-f<i;<i;(A-BV + CVV) 

 exiftente dv + ?vdx+Qvvdx+Rdx-o i $- e -M-*"®>)d* 

 et V—fQSdx.. 



Problema ro. 



61. Propofita aequatione differentiali praecedente : 

 dy -\- ?y dx -{- Qyy dx -+- R d x — o 

 innenire functiones L , M et N ipfius r, vt ea per 

 formulam Ljy-t-Mj-t-N diuifa fiat integrabilis.. 



Solutio. 



Cum igitur integrabilis effe debeat haec fbrmula :; 



dy -+- dx' K ?y-4-Q,yy -f- R } 

 Ly y -+- M y -4- N, 



per proprietatem generalem effe opportet , poflquam per 



(Lyy -+• My •+- N f multiplicauerimus :. 



y : yd-L _r£M' d N _. ~i" QM/J- ft R Lj/ -f- N P 



d. x *-* dx — _ p L yy + „ Qftj _ R M 



Vnde pro determinatione funclionum L , M et N has, 

 confequimur aequationes : 



I. dL^?Ldx-Q_Mdx 



II. dMzz:2RLdx-2QNdx 



III. dN—RMdx-VNdx r 



ex 



