The function satisfies and

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

The function yy satisfies dydx=2xx2−1\dfrac{dy}{dx}=\dfrac{2x}{x^{2}-1} and y(2)=0y(2)=0. Which expression represents y(x)y(x) for all xx with ∣x∣>1|x|>1? (a) ln⁡∣x2−1∣3\dfrac{\ln|x^{2}-1|}{3} (b) ln⁡∣x2−1∣\ln|x^{2}-1| (c) ln⁡(∣x2−1∣3)\ln\left(\dfrac{|x^{2}-1|}{3}\right) (d) ln⁡∣x2−1∣+ln⁡3\ln|x^{2}-1|+\ln 3

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