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 October 25th, 2011, 09:00 PM #1 Senior Member   Joined: Sep 2011 Posts: 140 Thanks: 0 fundamental question I noticed when I was solving differential equations, the constant value seems to confuse me a little. For example: $\frac{dy}{dx}= 3y$ $\frac{1}{y} dy= 3 dx$ if we integrate both sides, it will give $\ln y=3x$, however I am confused to whether put $\ln y + c= 3x+c$ or $\ln y=3x+c$ can anyone explain where to put the constant??
 October 25th, 2011, 11:27 PM #2 Global Moderator   Joined: Dec 2006 Posts: 21,037 Thanks: 2274 Let's assume that y > 0, so that you know y is not zero when you divide by it. When you integrate, you could give $\ln y\,+\,c_{\small1}\,=\,3x\,+\,c_{\small2},$ but that is equivalent to $\ln y\,=\,3x\,+\,(c_{\small2}\,-\,c_{\small1}).$ It therefore suffices to provide a constant on only one side of the equation. From the above, $y\,=\,ce^{{\small3}x},\text{ where }c\,=\,e^{c_{\small2}{\small-}c_{\small1}}.$

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