what is stable and unstable solution
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If the difference between the solutions approaches zero as x increases, the solution is called asymptotically stable. If a solution does not have either of these properties, it is called unstable.
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If a system is in a stable condition, a small perturbance of its parameters will not bring the system out of equilibrium.
If a system is in an unstable condition, any small perturbance will put the system totally out of equilibrium.
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