1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook