Abstract
We consider linear differential equations of the second- and the third-order and nonlinear second-order differential equations related via the Schwarzian derivative. The main objective of the paper is to obtain relations between the solutions of the second- and the third-order linear differential equations and the solutions of the nonlinear differential equations of the second order. The method is based on the use of the Schwarzian derivative, which is defined as the ratio of two linearly independent solutions of the linear differential equations of the second and the third order. As a result, we obtain new relations between the solutions of these linear and nonlinear equations.
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