The equation I'm trying to solve is(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{dy}{dx} = \frac{y^2 - 1}{x^2-1}[/itex], given y(2) = 2

The methods I'm somewhat familiar with are separation of variables, integrating factor, and exact. I tried this:

[itex]\frac{dy}{dx} = \frac{y^2 - 1}{x^2-1}[/itex]

[itex](x^2 - 1)dy = (y^2-1)dx[/itex]

[itex](x^2 - 1)dy - (y^2-1)dx= 0[/itex]

So, now it's an exact equation, right?

I tried integrating each part:

[itex]\int (x^2 - 1)dy = (x^2-1)y+c1(x)[/itex]

[itex]\int (y^2 - 1)dx = (y^2-1)x+c1(y)[/itex]

But now I'm confused what I'm supposed to do! If I just let the constants of integration be zero, then I have:

[itex](x^2-1)y[/itex]

[itex](y^2-1)x[/itex]

But what do I do with those?

I'm really confused :(

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# Really need help with a simple ODE

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