During solving the differential equations, why do we always drop the absolute value? for example for this problem (1-x 2 ) dy/dx = 2y we drop the absolute value from 1-x/1+x, during the end of the...

During solving the differential equations, why do we always drop the absolute value?

for example for this problem (1-x²) dy/dx = 2y

we drop the absolute value from 1-x/1+x, during the end of the solution? I know natural log has domain restriction. But for some of logs, there can be some negative values.