Exponentiating expression containing ln(abs(x))I am trying to figure out when we write +/- after exponentiating expressions containing natural log.So, say that we have integrated (1/x) with respect to x. Then we have ln(abs(x)) + C. That is, ln(x) with absolute value signs around the x.Now, if this is the left-hand side of the equation and we want to exponentiate both sides in order to solve, do we need to have +/- exp expression due to the absolute value inside the natural log?I am confused about when you need the +/- because in a WolframAlpha solution to a Diff EQs problem that I’m working on, they just took the positive expression instead of using +/-.But some problems in the book have answers with +/- for a similar process, so I am confused.

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Ashton Conrad · Accepted Answer

Step 1For the exercise in question, there will be no absolute value in the general solution because that is taken care of by the arbitrary constant of integration.Given:&amp;nbsp;&amp;nbsp;dy&amp;nbsp;&amp;nbsp;dt&amp;nbsp;=4y(y+2),,y(0)=6As you point out, this is separable.Step 2Rewriting, we get(1y−1y+2)&amp;nbsp;dy=8&amp;nbsp;dtln⁡|yy+2|=8t+c|yy+2|=e8t+cyy+2=±ece8tyy+2=ke8tNow there is no absolute value in the general solution since the constant of integration, k can be either positive or negative.

Exponentiating expression containing ln(abs(x)) I am trying to figure

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