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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 16r, page id 00068196:0031
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solutio hujus aequationis differentialis d
aadu +  Re  2ydx 4 aW dx = 0, à me
tudum reperta eodres aguecissime pcipe positi
Z et 10 dari ex X; potest ex hoc simplicissimo
priacipio derivari quod aequationem possumus mudi-
plicare per ai quidvis. Unde a si hanc
multiali et quidem ita hanc per aliquam v
danda x assumertiam dandam didem ex X ut
pars
quae
memorum quod continet affettiones ab y, fial summa
bilis, quoniam  tempe ea pars ex duobus
tantum constat membris quorum e in uno
affectio ipsiusy est diffepentia alterius debentus
tantum coefficientes re lationem inter A de bitan
habere, quod efficitur multiplicando. Multipli
cemus ergo equationem per v, et fiet
aa v dy + bZydx + aWD ax = 0. cm
sit formula aa  cujus differentia est
s
aam d aam sit formula aam, cujus
ifferentia est cmau 4 aa dm y unde
comparando fiet m= D, et  am = dv,
d
et vyax = aado. adeoque fit l
- 7dx seu aalogs. V=
avdy
ZdX Expertus
sum an tonnala data multiplie ut adu +Zydxtalot
posset reddi differentiabilis multiplicando perme mytor
sedres commode non successit, fiet sane ocamydu +
gomydy + a iz exgu tacen dy +aWmOdx y HanWdx
den prior coa possit
+
+an Z0 axu
cum diffeentia ipsius amgus, quae est damdu + agvam, et
siet mu sed tunc nonta quia vudque non est cum sud compare
nemue i y ideo oportat messe constantem, vel  pro myra
scuibi deberet y+ anim adeoque pro n.m supponiposset una quat
quantitas inde non ad sunt suficientes assumtitiae pro suobus
reliquis paribus gdus et gu, ilemque du et Y. Notandum hu etiam
aliuu habere comparem nemne dus dy.V et (dy:y seu formuta
may +mdy sdy. y +  am sdy: y est summabilis