Final answer:
To solve the given differential equation dy/dx = x/(1 - y²) by separation of variables, multiply both sides by (1 - y²), integrate both sides, and solve for y.
Step-by-step explanation:
To solve the given differential equation by separation of variables, we need to separate the variables x and y on either side of the equation.
We have dy/dx = x/(1 - y²).
First, multiply both sides by (1 - y²) to get (1 - y²)dy = xdx.
Next, integrate both sides with respect to their respective variables. The integral of (1 - y²)dy can be found using partial fractions and the integral of xdx is straightforward.
Once you have integrated both sides, solve for y to find the solution.