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Tumor growth

  1. Oct 11, 2004 #1
    can any one show me how to solve this equation that represents the tumor growth
    ds/dt = - a s ln(bs)
    where a and b are constants
     
    Last edited: Oct 11, 2004
  2. jcsd
  3. Oct 11, 2004 #2

    Tide

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    First, change variable to u = bs which gives

    [tex]\frac {du}{dt} = -a u \ln u[/tex]

    which you can integrate by setting

    [tex]\frac {du}{u \ln u} = -a dt[/tex]

    so that

    [tex]\ln \frac {\ln u}{\ln u_0} = -a t[/tex]

    where [itex]u_0[/itex] is the initial condition. You can exponentiate both sides twice to obtain an explicit solution for u(t) and finally s(t).
     
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