Mathematics

Mathematics

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

Browse the problem library