# Homework Help: Find the solution to the differential equation

1. Oct 23, 2011

### Yaaaldi

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.

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. Oct 23, 2011

### dynamicsolo

Do you know the method of integration by partial fractions? That is what you'll need for $\int \frac{1}{x^{2} - 1 } dx$. (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