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Quick question about simplifying a differential equation?

  1. Feb 5, 2012 #1
    I have solved this equation but I am just not quite sure why this final result is the way it is.

    [itex]\frac{2e^{t}+C}{e^{t}} = 2e^{-t} + C[/itex]

    Why is it [itex]e^{-t}[/itex] when its simplified ?
     
  2. jcsd
  3. Feb 5, 2012 #2

    wukunlin

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    Gold Member

    uhhh, how did you get that?

    shouldn't it be...
    [itex] \frac{2e^{t}+C}{e^{t}} [/itex]
    [itex] = 2 \frac{ e^{t} }{ e^{t} } + \frac{ C }{ e^{t} } [/itex]
    [itex] = 2 + C e^{-t}[/itex]
     
  4. Feb 5, 2012 #3
    I also got e^(-t) = -1
     
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