Determine the general solution of the differential equation dydx=1x2−1\frac{dy}{dx} = \frac{1}{x^2 - 1}dxdy=x2−11 for ∣x∣>1|x| > 1∣x∣>1.
y=12ln∣x−1x+1∣+Cy = \frac{1}{2} \ln|\frac{x-1}{x+1}| + Cy=21ln∣x+1x−1∣+C
y=12ln∣x2−1∣+Cy = \frac{1}{2} \ln|x^2 - 1| + Cy=21ln∣x2−1∣+C
y=arctan(x)+Cy = \arctan(x) + Cy=arctan(x)+C
y=12ln∣x+1x−1∣+Cy = \frac{1}{2} \ln|\frac{x+1}{x-1}| + Cy=21ln∣x−1x+1∣+C