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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 10v, page id 00068199:0020
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dy: dx = 2x + yy,. aa
p
_ fis gionaD naa y  12aa yy
a 20Xx +Z1XXy + 22XX yy
son
sit dy: dx = 10+ 11Y + 18Y
+20yy + 21y + 22y
compendio 30 + 31 y + 32 yy + 33y+34 y =0
d+  =V
a b + dD = 0
-D -dD: +C. fit
Unde pustra sex sumae
d30 + d31y + 314 +432 yy + 32Gdy +33 p 13339y dy + 434y + 4. 34y dy
yi
siet -dy = d30 + d31y + d32yy + d33 7 + 349 = Xx 4.
1) + 2.324 3. 33,+4. 34y
 ast
aa
ade sit a quatio  conferenda aequatim O multiplicatiae per
multiplicando illam per m + ny fient summi dermini,  _, 3 m y + 34ny
ab una parte e ab altera 4. 34p y + 333pXX 1
et sit p  n 
aa
33n y4
et 3. 33pXX = 34m + 4. 33P
constans
sit. 34 in Constanti ratione ad 33 fiat rx habebitur a p: M
a
ua
ta
supersunt ergo aequationes pro y, yy, y, 9, numero 4, pro quibus
2. Pro quibus
aosunt literae arbitrariae 30, 31 32, 33
biem prodeum equationes d ferentrates
quae in fellor folvi possunt
Mimi gradas
somplices plurm
incognitarum quae ebuci possunt ad aequationes differentrales
simplicesdem, quarum quaelibet sit unique incognitae
totidem
qualiones sunt 4, tollantur d31 et 432, habentur duae aequitione
in  8 in quibus 30, 31, d30 431 32,33. Unde differentiando
abebimus 132, et33 30, 31 d30, d31, dd30, dd3 ita jam
lavebim 54q. duas in quibus 30, 31 d30 d3, ad30, dd 31
sed ita ut tollatur ad30 et d d30, 4 veui descendum ad 3
 rursus ad dd20
130, d. 30, d130
Iti lindem aderi aequalio ubi  3C, d30
si jam eo
sit X+ X 30 + XX d30 + X dd30 = 0
1
a
idendum an arbitrariae sufficientes
 si 30 est rationalis gradus n erunt termini graducum n + 1., A et arbi
nariae lolidem, sed si sit XX30 + XXx d30+ X dd30 + x nen licet
assargitur altiu unde et judicari pte quid possibile et quo casu. Nam
aquaatio reddenda deurca
20+219f229y
C
∞d6 - - 49