# Homework Help: Need Help with Integration for Solving ODE

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1. Mar 31, 2016

1. The problem statement, all variables and given/known data
$$\frac{dy}{dx}=y^2-1$$
$$y(0)=3$$

2. Relevant equations
$$\frac{dy}{dx}=f(y) \leftrightarrow \frac{dx}{dy}=\frac{1}{f(y)}$$

3. The attempt at a solution
$$\frac{dx}{dy}=\frac{1}{y^2-1}$$
$$dx=\frac{dy}{y^2-1}$$
$$\int dx=\int \frac{dy}{y^2-1}+C$$
$$x=\int \frac{dy}{y^2-1}+C$$
How do I integrate $\int \frac{dy}{y^2-1}$?

2. Mar 31, 2016

### Staff: Mentor

3. Mar 31, 2016

### Buzz Bloom

I will give you a hint. think about factoring y2-1 = f1(y) × f2(y).
Then think about finding A and B such that 1/(f1 × f2) = A/f1 + B/f2.

Hope this helps.

Regards,
Buzz

4. Mar 31, 2016