Suppose I'm at this point in solving a differential equation and the initial condition is Q(0) = Q(adsbygoogle = window.adsbygoogle || []).push({}); _{0}

-ln|25-Q| + c1 = rt/100 + c2

Then if I combine c2-c1, I can rename it to c, we have:

-ln|25-Q| = rt/100 + c

Now if I multiply the equation by (-1), I get:

ln|25-Q| = -rt/100 - c

If I let -c = C:

ln|25-Q| -rt/100 +C

But if I rewrite -c = C, all the signs are reversed when I solve for Q. Also solving for the constant, my book kept the -c, and got c = Q_{0}-25, but when I rewrite -c to C, I get C = 25-Q_{0}.

So my question is, when can I rename constants? When I combined two constants it is okay to to rename the constant, but why is it incorrect when I negate a constant and rename it?

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# Renaming constants

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