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dy/dx = y(y-1)(y+1)

We can separate the variables, break the integrand into partial fractions, and integrate the fractions easily.

Solving gives y = the square root of 1 / (1 - e^(2t)).

as t goes to infinity, y goes to zero which the steady state solution.

But, the actual wording of the problem goes like this.

Find the steady state solution of the differential equation WITHOUT determining the exact solution and taking t to infinity.

How can that be done? Please help. Thanks.