) 70 ( &£a 



d* P -+ X d 1 P + X' <P P-f jx ^P+l^^-f^P-M/P^-f ? P+>'P -O. 

 lidcm vero valores in coefficicntibus diflfcrentialium ipiius x 

 introducti, fcqucntem exhibebunt acquationem: 

 d , x-\-(a-\-p)d'x->r-(ap-a}$-\-y-\-V)d i x 

 (a3'-a'£-f-f3'y-p'y-f-e-h4'W.v 



(aV-a^-^-py-p^-hyV-y^-hfe-Seijddx 



My^-Y^^-^^-^dxM^-^^^-^)dx 



-f-(v)0' — v)'0).x— o. 

 §. ii. Operae pretium iam eft, vt difpiciamus quomo- 

 do valores cocfficientium pro diflferentialibus, d'x, d'' x. etc. 

 expedite formari queanr,quippe quum hincenidcnsfietquomo- 

 do idem ncgotium, pro aequationibus altioribus perficerc li- 

 ceat. Quum igitur aequationcs noftrae propofitae fuerint: 

 d*x-\-ad z x + $d z y-\-y d dx + S ddy + e I x + ldy -f Y].v-f 0y=o 

 d l y -\-a'd z x-\- fidy -f y'd d x -f 5 'd dy -f e'd x -f ^dy-\- V-v-f 0^_o . 

 Notentur coefficientes differentialium ipfius x, qui funt : 



a, a', y, y'> e > £ '> ^ V 

 itemque coefficientcs differentialium ipfiusj fcqucntcs : 



p, (3', <5, *', ?, {', e, 9>. 

 Tum vero obfeructur in coefficicntibus differentialium pro jr, 

 aequationis noftrae finalis, primum occurrere has fummas fim- 

 plicinm cocfficientium: 



--+-£'; y -*-*'; i-4-jPi v,-f-0'; 

 quarum prima coefficientem differentialis <f jr conftituit, fe- 

 cunda vero coefficientcm differentialis d'x, tertia coefficientem 

 differentialis d x et quarta coefficientem diflferentialis^\v ingrc- 

 ditur. Porro fcqucntia formentur producta, binorum coeffi- 

 cientium: 



ap'-a(3'; a<$'-a'£; a£'-a'£; a0'-a'0; 



p' Y -[3y'; f3'e-f3e'; p'v)-pV; 



y<5'-y'<5: y£'_y'£; y e'- v '9- <5' £ -£e',cl'v]-<$Vi 



e<,'-e'<;.e0'-e'0i ?*-<V. ■*1»'— >l«'i 



quae 



