The differential equation has which of the following as its general implicit solution?

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

Problem

The differential equation dydx=(y2−1)sin⁡x\displaystyle \frac{dy}{dx}=(y^{2}-1)\sin x has which of the following as its general implicit solution? (a) ln⁡∣y2−1∣=−2cos⁡x+C\displaystyle \ln|y^{2}-1|=-2\cos x+C (b) ln⁡∣y+1y−1∣=−2cos⁡x+C\displaystyle \ln\left|\frac{y+1}{y-1}\right|=-2\cos x+C (c) ln⁡∣y−1y+1∣=−2cos⁡x+C\displaystyle \ln\left|\frac{y-1}{y+1}\right|=-2\cos x+C (d) ln⁡∣y−1y+1∣=2cos⁡x+C\displaystyle \ln\left|\frac{y-1}{y+1}\right|=2\cos x+C

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