I have noticed that if you have an equation (after integrating) such as
$$\ln|y| = \ln|x| + c,$$
and you further simplify it using the law of exponents, you get
$$e^{\ln|y|} = e^{\ln|x|+с},$$
which is the same as $y = cx$.

My question is why the absolute value disappears all of a sudden.

Edit: The original questions is:

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> Solve the separable differential equation: $(1+x)dy - ydx = 0$.
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> Final solution: $y = c(1+x)$.
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