Related papers: Autonomous first order differential equations
We prove that the main examples in the theory of algebraic differential equations possess a remarkable total differential overconvergence property. This allows one to consider solutions to these equations with coordinates in algebraically…
In this paper the necessary and sufficient conditions for a mapping to be the dependence of the complete solution of some differentiable first-order ordinary differential equation on the initial Cauchy condition are deduced. The result is…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
We study a particular class of autonomous Differential-Algebraic Equations that are equivalent to Ordinary Differential Equations on manifolds. Under appropriate assumptions we determine an easy-to-use straightforward formula for the…
We study the behaviour of solutions of ordinary differential equations of the second order with singular points, where the coefficients of the second-order derivative vanishes. In particular, we consider solutions entering a singular point…
An algebraic criterion that is sufficient to establish the existence of certain a priori estimates for the solution of first-order homogeneous linear characteristic problems is derived. Estimates of such kind ensure the stability of the…
We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…
I begin from a particular field of generalised Puiseux series and investigate a class of nonlinear differential equations in the field. It is appeared that the main part of differential equation determines solvability and positions of…
We consider linear n-th order stochastic differential equations on [0,1], with linear boundary conditions supported by a finite subset of [0,1]. We study some features of the solution to these problems, and especially its conditional…
We utilise recent results about the transcendental solutions to Riccati differential equations to provide a comprehensive description of the nature of the transcendental solutions to algebraic first order differential equations of genus…
This note is devoted, after the result of Harui, arXiv:1306.5842, to solve some natural questions for non-singular plane curves of degree $d$ over an algebraically closed field $K$ of zero characteristic.
A special class of autonomous algebraic differential equations is studied. No equations in the class have any entire transcendental solutions. In a sense, for almost all equations in the class, transcendental meromorphic solutions can also…
This article is devoted to the study of solutions of non-homogenous linear differential equations having entire coefficients. We get all non-trivial solutions of infinite order of equation $f^{(n)}+a_{n-1}(z)f^{(n-1)}+\ldots…
Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering…
Let $dx_i/dt=f_i(x_1,\cdots,x_n)$, ($i=1,\cdots,n$) be a system of $n$ first order autonomous ordinary differential equations. We use E. Cartan's equivalence method to study the invariants of this system under diffeomorphisms of the form…
In this article, we study systems of $n \geq 1$, not necessarily linear, discrete differential equations (DDEs) of order $k \geq 1$ with one catalytic variable. We provide a constructive and elementary proof of algebraicity of the solutions…
We introduce basic aspects of new operator method, which is very suitable for practical solving differential equations of various types. The main advantage of the method is revealed in opportunity to find compact exact operator solutions of…
These notes aim to provide a classical approach to solving some conformable differential equations based on prior knowledge of how to solve ordinary differential equations. That is, using the methods of separation of variables, homogeneous…
In this article, firstly we develop a method for a type of difference equations, applicable to solve approximately a class of first order ordinary differential equation systems. In a second step, we apply the results obtained to solve a…
The explicit solution of the initial-values problem is exhibited of a subclass of the autonomous system of 2 coupled first-order ODE s with second-degree polynomial right-hand sides, hence featuring 12 a prior arbitrary (time-independent)…