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Find the Function y(x) which satisfies dy/dx= 1/(xy^(2)) with the initial condition y(-1)=(-3) and state an...

Find the Function y(x) which satisfies dy/dx= 1/(xy^(2)) with the initial condition y(-1)=(-3) and state an X-interval where the solution is certain to exist.

I already solved the seperable function and applied to IC to get y^(3)/3 =ln(abs(x))-9 but am unsure how to find the interval

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