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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 80r, page id 00068196:0157
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 Z. Aequatio diffeaentialis simplex unius literae soluta est, velut by+ edyte-0
Quaeritur  aequationes differentiales siumplices bi polyliterae solvi possint. Incipiemes e biliter
quomodo
ZfF g ~ quas redecaluis ak has nihiulars terbnitiorum
incipiamus a biliteris easue reduco ad has mini minimor
atim
nempe etsi duplicese revera unius literae, et si in specieno marturium, quarum
duus dqZ + pdy + 9d7 + Y
ex his faciamus duas unam sine az alteram sine dy, et has aequando prioribus
dualus habetitur quaesitum Modum coincidentiandi singularem exhibui alia in scheds
sed subulatie plo hileterise Revera de potuisset issumi generalius ide modo
BEly + BdmZ +Bldy+ (3mdz +n
+ py+ qu
-0 et
sed qor
+ ipy+. Vdgque + V Vpdy + V9dZ + Y
sid puo modus videtur pre generati cc sufficere.
sed quid de trilteris. Sunto biliteae tres
110Y + 120Z +  1F1 dy + 141 dZ + 100) ( 0b
2109 +230 V + 2.+ 1 dy +231 dv + 200 -0
3207 + 330 + 321 di + 331 dv + 300 =0
Honc fiant tres aequationes quarum
quaelibet habeat tres absolutas, sed
una solam du, altera solam du, tertia
solam du, ita quaevis aequatio
postulat compurandas
porro tres datae possunt revocari ad eandem. itaque ut quaeratur coinciden
tiatio, considerandum est, habe esse terminos coincidentiandos semper 4
fient duodeum coincidentiationes, et revera videntur adesse arbitrariae
sufficientes, et quod mirum ad hoc nulla opus est quaesitarum differen-
Forte tamen res, hoc modo facilior:
videamus an non eademars ad biliteras applicari possi
sunt datae pls +peZ + pedus ips =0 vel ex datis factae Aby+ AZ + Aedy + asf - 0 et
19) + +hZF 4iaZ + aK -0, ubi b, 1,e, 518, a, ik, datae, B et . quaesitae
Rursu date
a nZ
8i
βdly BmZ
1go lZ + m dy + m dZ tan=
+ Bldy+ ( maqz +, B = 0
gnoptnque G 1y) + n q sn 0
17Py 197
0
7 ipgs pluque +Y pdys L 19 dZ vat = 0
x + Vague (- dy) - 8247 - 2ar -
Egy Ehy  idz
au d
aa aa
am na
il ip
mtr ot-gm, am  B dq
heet
à
nabelum . B, ibis habetur ), sed ex altera aequatione habebitur idem
cait p
ita un a suprep aequatio pro to m, e, q um adhuc semet, vtriusque valor
1
ubi 
ita habemus binas aequationes, pro + literis l, m, P, G
pro Quadrilters, et quatuor datis equationibus habebimus literas
Ex alte a 8. β = h. i - qul imp - am: m - 1q + 1qY: ErpV + dq. mp
sumemus quatuor aequationes, quarum quaevis sit trilitera
4 - 1
et rurjus G. β = omq: il - 9g: ip - dl: l +. Y. d rux: p.
et V. ) = mo - 34 - al + dP - h + hlg + dm - ldq 9 1) mp
n
n
 B. B - 3u - 32 - 1 + de  x + nic  9)  1t + de -  + 119 + dm - 1 9
n
mp
114
mp
imp
1 = 1
q= mb pe - h B ta + dm - 14q :, mp
+ apl9
Hi ortores  et 8 possunt haberi ad huc semel sed praestat  i fallor quaerere prius m, l,
(fi 8 -
s
Harum quamlibet multi pliao per arbisuariam propriata. Assumo deinde ractabis
aly q + ldy + imdZ + re =0 altera est tpy + 92
una est ly + m+ L
ly + mZ
tiata.
 a
la qu-
ut glas, et postea reservare  et d, si forte opus sit ad reddendas aequalines
altimas tractabiliores
modu
videtur
sufficere