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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 195r, page id 00068196:0385
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si aequatio differentialis sit, quae non in qua aliqua differentia
non ducatur in suam integralem ea replicatione infinita
non incommoie tractari potest.
sit du = a+ lx + Cy4 e dy = mdx + nydx  posito in et n dari per x, utcumque
fiet y = smex + fn smendy x Sn smaxdx 1 snydx
fiet y = Smax + Sn yax = (max + Snfmax  + Gnibsnysu =
sindx + snpsmax  + Indx snax smax + suex sax suyax
Eogo y = (ndx + suax smax + suax snox smtx + suctx snax suax siudx
Si sit du = mdx + n dx y + pdx yy. fiet
y = smax + sndx y + Spax yy = smdx + suax smax + sudx smaxus + Sn _  sper yy +
Spax. qusnex + pax 25mex snaxy + spud p  ly + s pax. qu spax yy
sed non puto hinc aliquid magnopere ad finitam solutionem duci
Ailiter ut non ascendamus ad summas, sed descendamus ad
differentias. Nempe ex aequatione erfferentiali per se vel
p adhibita differentio differential quaeramus y ratio naliter
eamque differentiando quaeramus et dus rationaliter, cumque valorem
substituendo in valore ipsius  habebitur y per X, dx, daque, nam ddx =0
inde simbiter tollumus dous, et ita pergendo habebimus semper accuratius
Exemplo utamur sit y =aadytax dx i adx + xdx + xdys
fiet du adx +X vel per conpoad. y = 13 - aadg:i2 + Xdu. Ergo siet
s
fiet
sit y
dy = 12 + Xdy, 413 = aa day ∞ - 13 - aadus d12 + Xddus + dx dy:, (E+ du
du 12 + dy orX L dus 2AX + p du = 12 diz - 12aadius + diz xdus C aa xdydaus)
13d12 = 13X ddy = 13dxdy + aady d12 (+ aady Xddy + nadu dX
quae aequatio si differentietur i poterit d ipsius dus valor rationalis
haberi, qui substituatur in ae vulore rationali ipsius y. Et eodem
modo mepertetur valor rationalis ipsius ddu, et ita porro