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Solve the separable differential equation

  1. Sep 3, 2009 #1
    1. The problem statement, all variables and given/known data

    dx/dy=-0.6y
    y(0)=5

    2. Relevant equations



    3. The attempt at a solution
    I tried solving it by
    [tex]\int[/tex]dy/y=[tex]\int[/tex]-0.6dx
    ln(y)=-0.6x+c
    ln(y(0))=-0.6(0)+c
    ln(5)=c
    ln(y)=-0.6x+ln(5)
    y=[tex]e^{-0.6x}[/tex]+5
    But its incorrect. I don't know what I am doing wrong. Can someone helping see what I am doing wrong? Thank You so much!
     
  2. jcsd
  3. Sep 3, 2009 #2
    You should solve for your function before substituting initial conditions. Remember that [tex]e^{ln|y|}=y[/tex]
     
  4. Sep 3, 2009 #3

    gabbagabbahey

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    Homework Helper
    Gold Member

    Is this a typo? Do really mean dx/dy=-0.6y, or do you mean dy/dx=-0.6y?

    If [itex]\ln y=-0.6x+\ln 5[/itex], then

    [tex]y=e^{-0.6x+\ln 5}=e^{\ln 5}e^{-0.6x}=5e^{-0.6x}\neq e^{-0.6x}+5[/tex]
     
  5. Sep 3, 2009 #4
    Okay. That makes so much sense. Thank You so much
     
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