The variable exponent Bernoulli differential equation (Q2292577)

In 1695 Jacob Bernoulli proposed a nonlinear differential equation \[ \frac{dy}{dx}+a(x)y=b(x)y^{p}, \] where \(p\) is any real number other than 0 or 1. The equation was solved by his brother Johann and by C. W. Leibniz in 1697, using different methods. Bernoulli equations are special because they are nonlinear differential equations with solutions expressible by Isaac Barrow's formula. The authors of the paper under review set a goal for themselves to investigate the existence of the solutions, in a spirit of \(17^{th}\) century mathematics, of a similar equation where \(p\) is no longer a constant but \(C^1\) function in a bounded interval \([\alpha,\beta]\), with \(p(x)\neq 1\) for all \(x\). The study is not well motivated by applications. No theorems are proved in the paper. All examples are superficial. Numerical simulations using MATLAB{\textregistered} \texttt{ode45} solvers don't reveal anything interesting.