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Exact Integration and Invertibility Completeness of the Nonlinear Relaxation Equation
We examine the nonlinear initial value problem $\dot{y} = C(1 - y^α)$ modeling polytropic gas permeation. For rational $α$, we derive the exact primitive via cyclotomic partial fraction decomposition, establishing its real trigonometric representation. By synthesizing Ritt's theorem with Rosenlicht'
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