Symmetry of solutions for some Bernoulli initial-value problems

Abstract

In this paper, we show that under certain conditions on the coefficients and initial values, solutions of two different Bernoulli initial-value problems are symmetric to each other either with respect to the t-axis, or the y-axis, or the origin. This knowledge of symmetry is very useful since solving one Bernoulli problem solves automatically the other. To the best of our knowledge, this interesting property has not been described in any other papers.