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!

Find the solution to the differential equation

  1. Oct 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the solution when x(1)=2
    dx/dt = (x2 - 1) / t






    3. The attempt at a solution


    I got all the variables to separate sides:

    1/(x2 - 1) dx = 1/t dt

    However I don't know how to integrate the LHS to get the correct answer.

    The answer book says:

    x = (t2 + 3)/(3 - t2)

    Is the answer in the book wrong? I don't know how to integrate 1/(x2 - 1) without using the trig identity which isn't in the answers..
     
  2. jcsd
  3. Oct 23, 2011 #2

    dynamicsolo

    User Avatar
    Homework Helper

    Do you know the method of integration by partial fractions? That is what you'll need for [itex]\int \frac{1}{x^{2} - 1 } dx [/itex]. (You could also use a trig substitution, but that's a bit excessive here...)

    You will also need to do some algebra because integrating your separated differential equation is going to give you t(x) , rather than x(t) .

    EDIT: Came back to this to finish working it through. The book's answer is correct.
     
    Last edited: Oct 23, 2011
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook