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Partial fraction? or using properties?

  1. Sep 7, 2010 #1
    1. The problem statement, all variables and given/known data

    dx/dt = 9-4x^2 , x(0) = 0

    when I integrate, am I supposed to use the property below?

    int du / (a^2 - u^2) = 1/2a ln(u+a / u-a) + c


    how do I integrate this by using partial fraction?

    tips anyone?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 7, 2010 #2
    You could use that integral to solve your integral. It would require some fancy footwork, so to speak, that is, getting your value of a correct.
  4. Sep 7, 2010 #3


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    You can integrate by partial fractions if you factor 9-4*x^2. Or you can use your formula after you do the u-substitution u=2*x. Your choice.
  5. Sep 8, 2010 #4
    using the property above, I get (1/12)ln((2x+3)(2x-3)) + c = t

    then, e^12t = (2x+3)(2x-3) + e^c

    e^12t - e^c = (2x+3)(2x-3)

    here how can I go further to have x equals to whatever.

    thanks a lot. it really helps.
  6. Sep 8, 2010 #5


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    You've got two mistakes there. i) Shouldn't it be (2x+3)/(2x-3)? Not the product? And worse, ii) When you exponentiate e^(A+c) you get (e^A)*(e^c), not e^A+e^c. Do you see where you did that?
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