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1 (1768) Methodus integrandi a primis principiis usque ad integrationem aequationum differentialium primi gradus / auctore Leonhardus Eulero
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C A P V T Y.

+4-7

ideoqne

dx ( x x y yj ___ du

77 + i je % » '

▼ode habebimus

, T *r 4

d\ 7 (M -sc N s x x -\-yy ),-f*0(x 4 4*xx yyA-y* ))

At est.

ce ^ 5 «

xx-hyy ~tt y etx*-hx x yy '4 -y* t*uiit

Notetur autem esse vade concludimus t

_ Uda , N t ! d t , O s U_ i Ou * d u

ü V iy. I* ^ _ *'* j. (y

sicque prodit integrando :

_ Mu i N_t* , 0 _f® O u*

V y- *T- 6 g . s y

Quodfi i am ponamus fieri y ~b si X~o , erit-- C " ~'~ ; tt a~ bVmA > tum

vero,

yV A-f-xV ( A- 3 rCbb)~zzb V{ A-f-Cxx)x^A-d-j A-d-C££)~6 t 7 ( A + Cyy) etb y A~x V{A-\-Cyy)+y V (A + Cxx).

Hinc cum sit:

»7 Mbxy , Hb(xx-i-yy)* t O b f xx -f -y y.) s . 03 * » >»

V / m 4 4 y mtA-HC66) "* s V (A-+-C) r V A

determi-

, cui satisfaciunt praecedentesinter functiones transcendentes , erit

Hbxy . N&'*^+>'y)* , Q.C xr-t >>)* , O bx*y 9

nostra relationationes ,

n t n _n . L n-JJi-y . n'J*-*-+ryj u t \jja~ j-

Hr 4 ^^c^>) 4 " 6 v.\ +-c&ö) "i" sva~

__ Q-? _

4 y; 4 -+"C 66 ) 6 y^ik-+-c^')

vbi

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