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Differential equation boundary conditions

  1. May 3, 2009 #1
    [tex]
    \frac{dN}{dt}=-k_sN^2
    [/tex]

    Attempt:

    [tex]
    \frac{1}{N^2}dN = -k_s dt
    [/tex]

    Integrate:

    [tex]
    -\frac{1}{N} + C = -k_s t
    [/tex]

    In the solution manual, C is written [tex]\frac{1}{N_0}[/tex]

    Why?
     
    Last edited: May 3, 2009
  2. jcsd
  3. May 3, 2009 #2

    dx

    User Avatar
    Homework Helper
    Gold Member

    If you integrate from 0 to t on the right, you have to integrate from N0 to Nt on the left, where N0 is the value of N at t = 0.
     
  4. May 3, 2009 #3

    Cyosis

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    Homework Helper

    Alternatively use the boundary conditions in this case [itex]N(0)=N_0[/itex] and then solve for C.
     
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