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Differential Equations without numbers

  1. Feb 5, 2013 #1
    1. The problem statement, all variables and given/known data
    Here is the whole problem.

    2. Relevant equations
    Not sure

    3. The attempt at a solution
    As you can see I got the first part. I solved the equation at part a.) for A(c) and plugged it into the D.E. and then solved for B(c). I need help on how to do the next part. How do I get B(0)?
  2. jcsd
  3. Feb 5, 2013 #2


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    B(0)=A(0)-L, right?
  4. Feb 5, 2013 #3
    I feel really dumb haha. Thank you, I was thinking they were looking for a number.
  5. Feb 5, 2013 #4
    Now I'm having trouble with part b.

    I'm solving dB/dc = -kB by doing it as a separable equation and getting B=sqrt(-2ck+2p) where p is the constant of integration. Then using the IVP of B to find P and plugging it back in to the equation I got. Once I solve for B I put it in the equation at part a. and solving for A.
  6. Feb 5, 2013 #5


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    The square root is clearly NOT a solution. If [itex]B= \sqrt{2p- n2ck}= (2p- 2ck)^{1/2}[/itex] then [itex]dB/dc= (1/2)(-2k)(2p- 2ck)^{-1/2}= -k/B[/itex], not "-kB". Do the integration again.
  7. Feb 5, 2013 #6


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    And showing what you are integrating would be helpful as well.
  8. Feb 5, 2013 #7
    I was integrating B dB when I should have been integrating 1/B dB

    I got it, Thank you!
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