Given : (a) list the equation of every vertical isocline (where the slope is…

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

Given dydx=y2−1x−2\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≤x≤40\le x\le 4 and −3≤y≤3-3\le y\le 3; (b) in one sentence, describe how these isoclines divide the rectangle into regions with different sign combinations for dydx\dfrac{dy}{dx}.

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