Purpose <p>The linearly evolving dynamics hidden in nonlinear systems provides crucial insights for understanding their diverse nonlinear behaviors; Existing studies, however, are predominantly confined to autonomous systems. This work addresses non-autonomous systems, automatically distilling <i>linear evolving dynamics</i> hidden in <i>non-autonomous systems</i>.</p> Methods <p>It is formulated as an iterative optimization scheme which synchronously identifies the coordinate transformations (linear or nonlinear transformations of state variables) and the linearly evolving dynamics governing the transformed coordinates.</p> Results <p>Numerical examples demonstrate the efficacy of this method to non-autonomous linear/nonlinear systems, and the results identified possess acceptable accuracy across a rather wide parameter range.</p> Conclusion <p>The proposed methodology distills the <i>linearly evolving dynamics</i> hidden in <i>non-autonomous nonlinear systems</i>, providing novel and instructive perspectives for analyzing such systems.</p>