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Differential equation

  1. Dec 14, 2011 #1

    georg gill

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    Gold Member

    [tex]\frac{ds}{dt}=600-\frac{2s}{200+t}[/tex]

    [tex]\frac{ds}{dt}+\frac{2s}{200+t}=600[/tex]

    [tex]\frac{ds}{dt}e^{ln(100+t/2)}+\frac{2s}{200+t}e^{ln(100+t/2)}=e^{ln(100+t/2)}600[/tex]

    [tex]\frac{d}{dt}(se^{ln(100+t/2)})=(100+t/2)600[/tex]

    [tex]se^{ln(100+t/2)}=\int(100+t/2)600dt[/tex]

    [tex]s(100+t/2)=600(100t+t^2/4)+C[/tex]

    t=0 s=20 000

    [tex]20.000\cdot100=C[/tex]

    But this is wrong

    I guess i want to know what I did wrong. I used the product rule for derivation backwards. Here is answer sheet

    http://bildr.no/view/1051423
     
  2. jcsd
  3. Dec 14, 2011 #2

    dextercioby

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    Homework Helper

    The integrating factor is wrong. Revise your calculation and look up the formula for it in the book.
     
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