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Why do they take the natural log of the integration constant in solving this differential equation?

Writer Andrew Mclaughlin
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I am taking a circuits class. My book is solving a first order differential equation for a RC circuit. Here are the steps they take:

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in the second step, after integrating, they end up with lnA as the integration constant. Where does that come from?

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1 Answer

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For the sake of an answer,

If $K$ is your constant of integration, you can write it as $K=\ln(A)$, where $A=e^K$. Nothing special here, it's just so when you subtract it from both sides you get a more convenient term $\ln\frac{\nu}{A}$ on the left.

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