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Renaming constants

  1. Feb 2, 2016 #1
    Suppose I'm at this point in solving a differential equation and the initial condition is Q(0) = Q0
    -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 = Q0-25, but when I rewrite -c to C, I get C = 25-Q0.

    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?
  2. jcsd
  3. Feb 2, 2016 #2


    Staff: Mentor

    You can simplify things a bit by including the constant only on one side (the right side).

    You lost an = in the line above.
    Whenever you want to.
    If -c = C, and the book shows c = ##Q_0 - 25##, then C = ##-(Q_0 - 25) = 25 - Q_0##.
  4. Feb 2, 2016 #3
    Check your math. Your calculation of c and -C are wrong.

    Looking at your last 2 equations, at [itex] t=0 [/itex] you either get [itex]ln\left|25-Q_0 \right| = -c [/itex] or [itex]ln\left|25-Q_0 \right| = C [/itex]. These two results agree with your definition [itex]c=-C [/itex].

    You can always define a new constant as a combination of multiple constants.
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