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Homework Help: 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


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    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
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