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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 17r, page id 00068196:0033
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solatio aequationis differentialis aadque + Bydx + at dx =0 a medudum
reperta est ex principio comparum terminctam eo jungendi compares terminos qui se javicem habere
possunt, ut sum differentia eabuesa et ferminu e difeentiatum. Hi termini enm hoc loco sunt y et dy
multiplicetur aequatio per h. fiet aahdus +hBydx + abhdx = 0 debet esse daah) = hBdx b
ut aahdus +tByax possit summari sin facere aahus et fiet aadh = hBdx seu dh: h = (Bdx: aa
Sit  aequateo aad raaβ dY + B  sWVdx +a) pax + aa D ax = 0 fiat
d
(
V = py: a et do = ody + rdp, a et vdo = ppydy + pyyap: aa
unde interpretendo et multipplicando per h
Appydy +ha p dy p gu ap +haβydp thaaddx  0
s
RAppyy axiaa +h) py dx
unde inter pretando fit
et mu
dchpp hp dp thappdx: aa seu 2) aa hpap + ac ppdh = (aa hp ap) + k. A Ahpp dX, et
Ex primo compare yy et ydy
fiet. aa h dp + na pdh = A hp ax. seu aa lous hp = fAdx. Ergo datur EP. quod
si esset X =0 foret hp = ab constanti.
lix primo compare yy et rydys, fiet d (hpp) = hp dp + AAppdx: na, adcoque fiet
aa hpdp, + =Aapp dh = Caa hp ap + AhppdX, et filt logu h = 2(Adx: aa quod si 
Li
up
quod si abesset A. foret h constans, seu dh =0
Ex secundo compare y et dy fit d (a Bh0) = a βh dp + ) hpdx
sed eu
sen a ap dCBh) F aBh dp = (a (hap, + Vhpax sed ita evanescit et p) adeoque non
et n= pay+ ydp + dr
et vdo= Oppysdy + 7ypap + 8prdy +ypdr +yrap + rar. Uade interprendo aequationea set
s
adsunt ert B apsbitrariae sufficientes.
G
inde haappudus thaapuyap thaaprdy thaaydx  rdr
p hic homogenea est mero)
t, quasi esset pia +hst ppyy ex
1a
haar ydp
haaBpdus haa By ap iha a βr
2D pryex  rrax
ha py dx tha) Ydx
et multiplicando per h.
Ex primo compare yy et 2ydy, fiet ut ante d sta apBx: 2) = a apdp + hst ep dx,
masong
+tiaaB ex
2 a aip dp)  aappdh = (2 aa hpdp, + 2 A h pp dx
seu 
seu dh: n = 2 5 dH seu logh = 2 (Adx: aa
Ex secundo compare y et du, fis act d h pdret h, apss Bdp t EA hpX+ ah) pdx (adhpY +h BP)
quod si abesset A foret dh constranu =0 seu h constans
A
acc prah+ aa Bpato aarhap + aar Bah ( aa Bhapi+ aa B pati nansab+ aanp ds3
la
sumus
aanparet aahrdp + aah βdp + 2) hlpr dx = aa d (lip. r+ C) =
seu
Epraaati
itaque datur 2. omnino.
e
ea
dx faared. het aa Bhaptaa β pantapa apaβ
e
sed
ande fit, BdhataB = ∞ son βh = ab
et a piet que jum habear