Mathematics

Problem

Given

\dfrac{dy}{dx}=\dfrac{y^{2}-1}{x-2}

: (a) list the equation of every vertical isocline (where the slope is undefined) and every horizontal isocline (where the slope is zero) that lies within

0\le x\le 4

and

-3\le y\le 3

; (b) in one sentence, describe how these isoclines divide the rectangle into regions with different sign combinations for

\dfrac{dy}{dx}

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