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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 299r, page id 00068196:0593
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(2)
dx: dy = a X - 2XXy, : 3a ay - 2Xyy seu 3aaydx - 2Xyydx = a xdy - 2xxy dy
seu aa = 2X yydx - 2XXy dy, : 3y dx - x dy. unde ut tollamus a, fiet
(5
5ydx - Xdy, fxyy dx (+ 4 X ydyd + Lyy dxdx - f xX y ddys - f xx dydys ( _ vy dr dy)
e
ZXVydx = XxXy dy, 3yddx + 3dydx - x ddy= dxdy, sed
2
(Sy, dx dex + Sy dxcxdx- Syyxx dx dey -(3y Xx dx dydy
e
(- 8 Xxyydy dex X e axdyX (+ X3y dus ddu
+ X dydydy
ex yyy dx ddx +Xyy dydxdx (-XXyy dx ddy
(3X X yu dy dax - 2 Xx y dydydx t XXX 7 dy ddy
seu fier
3y dx - yx dx dys + X du - 3 Xy dy  = 2yx dx ddy - 2 X 5 dyddx
17) (dx adu = dy ddx 18))  ds
dx
ex
jam d F adhuc aliter haberi potest per eg. 1. et fiec aeg. 9 cuope
29yXX dx
ex
valore ut duos valores et a + ex aeg. 7 et comparando, fiet
lis
ex
aequati in valor ipsius dx: dus sed quem puto coincidere debere priori
eduarum literanum decundi gradus
Cmnis aequatio diferentialis constat ex sequentibus termonis
 quantitalibus X: y, dx: dy, adx: ddus, X ddx: dx,
X ddg: dy, xddu: Ax, X ddy: du, y ddx: dx yddx: du,
y ady: dx, y ddy: dyt
posita ex constante
aeRKyZ: a = EXC B coGPirngr sit. dy: _v et data
equatio 1o+ ny + n Y etc + ∞8  21V + 22V, etC +  HY.  9,V.) 13 1
2
+10 yY 12C yVy V yPr eu + 22( 00 + Ory + 03y + 0
_ a +bB cy + dx. a + by + cV + OYV, + C y +f V + g7 v+ hYv CH =0
a
(abi b, et c dantur ex x; fingenda est aliu aequalio ipter V et
quoe sit l+ my + nP + p y2+ 9Zy +YZV et C=0 cujus quoratur
differentalis (posito C, n n, p, ecc constantes) et sit dusdus =Cet v
v:a = sib y:a