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DSolve[2.56 x''[t] == -0.32 x'[t] - x[t] - 0.05 x[t]^3 + 2.5 Sin[t], x[t], t]

I want to find the solution and find two initial conditions such that their corresponding steady-state solutions are different.

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    $\begingroup$ DSolve returns your input unchanged, which indicates that it does not know how to solve your equation. If you have a reason to think that an analytical solution should exist, and what form it might take, please share it with us. Otherwise, you might be out of luck for an analytical closed form solution. You can of course solve it numerically though. Consider that you would like a parametric solution, depending on the values of the ICs, ParametricNDSolve might be helpful. $\endgroup$ – MarcoB Jan 13 at 4:20

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