Find the solution to the differential equation

[Yaaaldi]

Homework Statement

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

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..

 

[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.