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# Title: LBr. 560 · L'Hospital
# Folio 52v, page id DE-611-HS-855907:0104
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-855907&page=104
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sotest
identificativae, et pro  iis  quantitatis quaesits 30, et 31
Aequationes sunt 20d30 10. 31 =  et 20 l3t  2 10r32 -H. 31 = 5
 20 130 n tC. 3t = O et 20d31  - H31 = 0
4 sit   a fit d31: 31 = n2o (1dx. 20
Aequationes sunt d30 - 10. 31 =0 et d31 = 11. 31 = 0. posit 20 =1
x hypothesi, et aliis literis coanescentibus et fiet
mmma
unm
o
d31 : 31 = (11 dx
et d30 = 10.31 adeoque 30 = 10. 31 dx. Ergo s data sit aequa
tio differentialis resolvenda: 10dx + 1y ax + dus =0 fiet aequatio
constructrix
quod desi deraint
1031d + 31Y = 0 posito (d31: 31 = sit ax. po es
fieri, ut aequatio talis possit revocabilis ad ordinarias, exempli causa
se
sit
e
Rvelalia ut labet sa
1 =  x 2: X fiet 31 = XX: a H a sit 10 = XX + ax,: aa ) sumablit
colva summobilitate,
ut fiet 10.3l dx = X + aX, dx: a et (10. 3) ax = q5aX
adeoque fiet 4XE +  AX + aAXXG 4X L SAXX KaG
adeoque fiet 4X + SaXX +  20 aa y =0.
4. 5
ubi 20 est numerius verus
quae proinde salisfaciet data XX + ax dx + 2aa : X ydx +ady = 0. sei
aequatios
recte caleaum subd. ut falculus ostendit. Quanquam et aliae ei satisfacientes
eodem modo reperici possint
Si aequatio differentialis construenda pro suo modalo generalis,
nisset 10dx + 1 y dx + 20dy + 21 ydy =0 quae est genendissiu
adeoque omnis aequatio differentialis in qua nec y nec dus assurgunt
ultra simplicem gradum, quicquid sit de quantitatis X habitudine,
constructa habetur
Tandemque Methodum debite
prosequendo assurgi potest ad altiores ipsius y potentas.
no et qsias dy.
posito
logari
tamum
ipsiqus a
esse 0