Integrable discretization of the Bernoulli equation with arbitrary higher-order accuracy

This study aims to derive an integrable discretization of the Bernoulli equation that achieves arbitrary higher-order accuracy while preserving the original solution structure. Using the Padé approximation, we develop discretizations for nonhomogeneous first-order linear differential equations with both constant and variable coefficients. By transforming the independent variable, we obtain the discretization of the Bernoulli equation and its general solution.