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The first segment stops after computing the first and second derivatives of the resonant trial solution $x=Ate^{-t}$. It does not yet substitute these derivatives back into the differential equation or solve for the unknown coefficient $A$.

Conditions: The segment covers the setup of the homogeneous solution and the resonant trial solution.; The derivatives $\dot{x}$ and $\ddot{x}$ are computed but not substituted.

The first segment stops after computing the first and second derivatives of the resonant trial solution $x=Ate^{-t}$. It does not yet substitute these derivatives back into the differential equation or solve for the unknown coefficient $A$.

Conditions: The segment covers the setup of the homogeneous solution and the resonant trial solution.; The derivatives $\dot{x}$ and $\ddot{x}$ are computed but not substituted.