Related papers: Explicit solution of second-order delayed discrete…
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
We solve some forms of non homogeneous differential equations in one and two dimensions. By expanding the solution into whell-posed closed form-Eisenstein series the solution itself is quite simple and elementary. Also we consider Fourier…
We introduce a hybrid Cole-Hopf-Darboux transformation to relate solutions of nonlinear and linear second order differential equations and derive a sufficient condition for this correspondence. In particular we show that solutions of some…
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining…
A discrete multidimensional system is the set of solutions to a system of linear partial difference equations defined on the lattice $\Z^n$. This paper shows that it is determined by a unique coarsest sublattice, in the sense that the…
In this paper, we introduce some analytical techniques to solve some classes of second order differential equations. Such classes of differential equations arise in describing some mathematical problems in Physics and Engineering.
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…
Infinitely many explicit solutions of certain second-order differential equations with an apparent singularity of characteristic exponent -2 are constructed by adjusting the parameter of the multi-indexed Laguerre polynomials.
We introduce a class of second order backward stochastic differential equations and show relations to fully non-linear parabolic PDEs. In particular, we provide a stochastic representation result for solutions of such PDEs and discuss Monte…
There are many methods for finding a particular solution to a nonhomogeneous linear ordinary differential equation (ODE) with constant coefficients. The method of undetermined coefficients, Laplace transform method and differential operator…
We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…
We give evaluations in closed form of certain non linear differential equations
In this paper, we describe the structural properties of the cone of $\mathcal{Z}$-transformations on the second order cone in terms of the semidefinite cone and copositive/completely positive cones induced by the second order cone and its…
We show that the higher order linear differential equation possesses all solutions of infinite order under certain conditions by extending the work of authors about second order differential equation \cite{dsm2}.
This paper studies the second moment boundedness of solutions of linear stochastic delay differential equations. First, we give a framework, for general $\mathrm{N}$-dimensional linear stochastic differential equations with a single…
Based on the analysis of a certain class of linear operators on a Banach space, we provide a closed form expression for the solutions of certain linear partial differential equations with non-autonomous input, time delays and stochastic…
A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs) which…
This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained…