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Absolute Values in Separable Differential Equations

  1. Mar 6, 2015 #1
    When solving a separable differential equation, my textbook says this:
    ln|v-49|=-t/5+C→
    |v-49|=e-t/5+C
    v=49+ce-t/5
    What happened to the absolute values? I think it has something to do with the exponential always being positive.
     
  2. jcsd
  3. Mar 6, 2015 #2

    SammyS

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    The equation ##\displaystyle\ |v-49|=e^{-t/5+C}\ ## is equivalent to
    ##\displaystyle\ v-49=\pm e^{-t/5+C}\ ## ##\displaystyle\ v-49=c\, e^{-t/5}\ ##, where ##\ c = \pm\ln(C) ##​
    So the new constant, c, (lower case) absorbs the ± .
     
  4. Mar 7, 2015 #3
    Ohhhh. HAHA!:oldlaugh: That was dumb :)
     
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