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Initial value problem using partial fractions

  1. Apr 5, 2008 #1
    (t+1) dx/dt = x^2 + 1 (t > -1), x(0) = pi/4

    I have attempted to work this by placing like terms on either side and then integrating.

    1/(x^2 + 1) dx = 1/(t + 1) dt

    arctan x = ln |t + 1| + C

    x = tan (ln |t + 1|) + C

    pi/4 = tan(ln |0 + 1|) + C

    pi/4 = C

    x = tan (ln |t + 1|) + pi/4

    Is this even close??
    This was supposed to be a partial fractions exercise but I'm not seeing how. Thanks for any help.
  2. jcsd
  3. Apr 5, 2008 #2


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    No, I don't see any need for partial fractions. For the record, you can integrate 1/(x^2+1) by factoring x^2+1=(x+i)(x-i) and get an expression involving complex logs that is equivalent to arctan. But I don't know why you would want to.
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