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In this short note, we review several one-dimensional problems such as thoseinvolving linear Schroedinger equation, variable-coefficient Helmholtzequation, Zakharov-Shabat system and Kubelka-Munk equations. We show that theyall can be reduced to solving one simple antilinear ordinary differentialequation $u^{\prime}\left(x\right)=f\left(x\right)\overline{u\left(x\right)}$or its nonhomogeneous version$u^{\prime}\left(x\right)=f\left(x\right)\overline{u\left(x\right)}+g\left(x\right)$,$x\in\left(0,x_{0}\right)\subset\mathbb{R}$. We point out some of theadvantages of the proposed reformulation and call for further investigation ofthe obtained ODE.

A short note on the appearance of the simplest antilinear ODE in several physical contexts