'AEQVJTIONVM DIFFERENTIAIIFM. 41 



Sit itaque conftans arbitraria Azz cofO, vt fit Brrfm.d 

 ct cafu, quo V (p(3- 40C y -\- \a)z^m V~ 1 , aequatio 

 realis erit 



^cof^-«fin.p=:^of.0-4-«fin.O feu q~-^^ ] 



53 raz cot. — t^ 

 Quare aequationis differentialis 



dy-t-yydx-\- T^ll^*$K == ° 



pofito p~f tt^$x-i-vxx > aequatio integralis comple- 

 ta eft 



2.{cL-\~$x-\-yxx)y~ (3-}-2 y^ -4- z» cot. ^ 1 ^ 



£ 



/• i(3-j-vAM-iWcot.- 



feu y =: -*- '— — 



a-j-fix-+-yxx 



Vel fit = 1 8o°-£et habebitur y =- r — ^^ 2- * 



Hoc autem cafu notandum eft , integrale fpeciale , ex 

 quo haec omnia deduximus , fieri imaginarium , quo 

 tamen non obftante inde integrale completum in fbrma 

 reaJi exhibere licuit. 



Exemplum 3. 



68. Vropofita aequatione W&caiianq dy-4-yydx 

 — ax m dx — o, pro cafibus exponentis m, quibus eam 

 feparare Iket , inuenire multiplieatores idoneos. 



Skyzzv valor aequationi fatisfaciens , et cum 

 fit Pzro, Qzzi , et Rz-flf, erk primus multi- 

 plicator, aequationem integrabilem reddens, 



— 2 Jv dx 



tj — W 



Tom.VIII.Nou.Comm. F per 



