The general solution of the differential equation (ex + 1)ydy = (y + 1) ex dx is :

1
(y + 1) = k(ex + 1)
2
y + 1 = e+ 1 + k
3
y = log {k(y + 1) (e+ 1)}
4
y = log\(\rm\left\{\frac{e^x+1}{y+1}\right\}\) + k

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