Answer
$\dfrac{y-1}{y+1}=cx^2$
Work Step by Step
In order to to solve the given differential equation we will have to separate the variables and then integrate.
Here, we have
$\int \dfrac{dy}{y^2-1}=\int \dfrac{dx}{x}$
or, $\dfrac{\ln [{\dfrac{y-1}{y+1}}]}{2}=\ln |x|+c'$
Then, we have $\ln [{\dfrac{y-1}{y+1}}]=2 \ln |x|+\ln c'$
Hence, $\dfrac{y-1}{y+1}=cx^2$
