# Search: Ordinary Differential Equations

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#### Alternative integration procedure for scale-invariant ordinary differential equations

For an ordinary differential equation invariant under a one-parameter group of scale transformations x→λx, y→λαy, y′→λα−1y′, y″→λα−2y″, etc., it is shown by example that an explicit analytical ... yield an analytically integrable transformed equation. AND PHRASES; Ordinary differential equations; Integration method; Scaleinvane - ALTERNATIVE INTEGRATION PROCEDURE FOR SCALE-INVARIANT ORDINARY

#### k-component disconjugacy for systems of ordinary differential equations

Disconjugacy of the kth component of the mth order system of nth order differenttal equations Y(n)=f(x,Y,Y′,…,Y(n−1)), (1.1), is defined, where f(x,Y1,…,Yn), ∂f∂yij(x,Y1,…,Yn):(a,b)×Rmn→Rm are ... variational equation z(n) ?n..i=ifyi( x' 0(x), Y0(n-l)(x)) Z (i-l), (1.2), is also studied. - K-COMPONENT DISCONJUGACY FOR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS Conditions are given for continuous

#### AN ALTERNATIVE TECHNIQUE FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS

In this paper, a new method for solving ordinary di erential equations is given by using the generalized Laplace transform Ln. Firstly, the authors introduce a di erential operator that is called the ... differential equations Example 3.1. We solve the following ordinary di erential equation (3.1) xz00 (2v + n 3)z0 + xn 1z = 0; k 2 N; v 2 N: solution: Dividing (3.1) by xn 1, adding and subtracting the term xnn

#### The Mathematics of Gossip

How does a lie spread through a community? The purpose of this paper is two-fold: to provide an educational tool for teaching Ordinary Differential Equations (ODEs) and sensitivity analysis through a ... be placed in groups or work independently to figure out how to add the alpha term ? the movement of individuals from the recovered population back to the infected population ? to the equations. This

#### Bounded index, entire solutions of ordinary differential equations and summability methods

A brief survey of recent results on functions of bounded index and bounded index summability methods is given. Theorems on entire solutions of ordinary differential equations with polynomial ... I nternat. J. Math. & Math. Si. Vol. BOUNDED INDEX, ENTIRE SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS AND SUMMABILITY METHODS G.H. FRICKE 0 1 2 Ee Solutions. 0 Department of Mathematics Wright

#### Bounded index, entire solutions of ordinary differential equations and summability methods

A brief survey of recent results on functions of bounded index and bounded index summability methods is given. Theorems on entire solutions of ordinary differential equations with polynomial ... I nternat. J. Math. & Math. Si. Vol. BOUNDED INDEX, ENTIRE SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS AND SUMMABILITY METHODS G.H. FRICKE 0 1 2 Ee Solutions. 0 Department of Mathematics University

#### Continuous dependence of boundary values for semiinfinite interval ordinary differential equations

Certain elliptic equations arising in catalysis theory can be transformed into ordinary differential equations on the interval (0,∞). The solutions to these problems usually depend on parameters ρ∈ℝn ... consequence, bifurcation results for the elliptic equation are obtained. lim f(C; u) - CONTINUOUS DEPENDENCE OF BOUNDARY VALUES FOR SEMIINFINITE INTERVAL ORDINARY DIFFERENTIAL EQUATIONS (Received December i0

#### Linear Operators and the General Solution of Elementary Linear Ordinary Differential Equations

We make use of linear operators to derive the formulae for the general solution of elementary linear scalar ordinary differential equations of order n. The key lies in the factorization of the linear ... introductory course on ordinary differential equations. The method is based on the integral operator as defined in Definition 2.3. and also applies to linear differential equations with nonconstant coefficients

#### Homoclinic solutions for linear and linearizable ordinary differential equations

(French). MR 99i:34082. [9] M. Cecchi , M. Marini , and P. L. Zezza , An abstract method for nonlinear boundary value problems on noncompact intervals , Ordinary Differential Equations and Functional ... . Zbl 283 . 34052 . [12] , On nonlinear functional perturbation problems for ordinary differential equations , J. Differential Equations 12 ( 1972 ), 63 - 80 . MR 48#6574. Zbl 243 . 34015 . [13] A. G

#### k-component disconjugacy for systems of ordinary differential equations

Disconjugacy of the kth component of the mth order system of nth order differenttal equations Y(n)=f(x,Y,Y′,…,Y(n−1)), (1.1), is defined, where f(x,Y1,…,Yn), ∂f∂yij(x,Y1,…,Yn):(a,b)×Rmn→Rm are ... variational equation z(n) ?n..i=ifyi( x' 0(x), Y0(n-l)(x)) Z (i-l), (1.2), is also studied. - K-COMPONENT DISCONJUGACY FOR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS Conditions are given for continuous

#### Alternative integration procedure for scale-invariant ordinary differential equations

For an ordinary differential equation invariant under a one-parameter group of scale transformations x→λx, y→λαy, y′→λα−1y′, y″→λα−2y″, etc., it is shown by example that an explicit analytical ... yield an analytically integrable transformed equation. AND PHRASES; Ordinary differential equations; Integration method; Scaleinvane - ALTERNATIVE INTEGRATION PROCEDURE FOR SCALE-INVARIANT ORDINARY

#### Object-Oriented Implementation of Software for Solving Ordinary Differential Equations

We describe an object-oriented implementation of numerical integration methods for solving ordinary differential equations. Software components that are common to many different integration methods ... INTRODUCTION The traditional way of writing software for solving ordinary differential equations (ODE) is to provide one subroutine to the user. The user calls this subroutine specifying the function that should

#### On periodic-type solutions of systems of linear ordinary differential equations

We establish nonimprovable, in a certain sense, sufficient conditions for the existence of a unique periodic-type solution for systems of linear ordinary differential equations. ... of linear ordinary differential equations. 1. Formulation of the problem and statement of the main results Let n1 and n2 be natural numbers, ? > 0, ?i ? Rni?ni (i = 1, 2) nonsingular matrices, and ik

#### Continuous dependence of boundary values for semiinfinite interval ordinary differential equations

Certain elliptic equations arising in catalysis theory can be transformed into ordinary differential equations on the interval (0,∞). The solutions to these problems usually depend on parameters ρ∈ℝn ... consequence, bifurcation results for the elliptic equation are obtained. lim f(C; u) - CONTINUOUS DEPENDENCE OF BOUNDARY VALUES FOR SEMIINFINITE INTERVAL ORDINARY DIFFERENTIAL EQUATIONS (Received December i0

#### Bounded index, entire solutions of ordinary differential equations and summability methods

A brief survey of recent results on functions of bounded index and bounded index summability methods is given. Theorems on entire solutions of ordinary differential equations with polynomial ... I nternat. J. Math. & Math. Si. Vol. BOUNDED INDEX, ENTIRE SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS AND SUMMABILITY METHODS G.H. FRICKE 0 1 2 Ee Solutions. 0 Department of Mathematics Wright

#### On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem

In the present paper we study nonlocal problems for ordinary differential equations with a discontinuous coefficient for the high order derivative. We establish sufficient conditions, known as ... Journal of Applied Mathematics and Stochastic Analysis ON NONLOCAL PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS AND ON A NONLOCAL PARABOLIC TRANSMISSION PROBLEM M. DENCHE 0 0 Universit de

#### Lie symmetry analysis of some conformable fractional partial differential equations

vector fields and the Lie symmetries are obtained. Moreover, exact solutions are given to these equations in terms of solutions of ordinary differential equations. In particular, it is shown that the ... properties of conformable derivative. Open Math. 13, 889–898 (2015)MathSciNetCrossRefGoogle Scholar 5. Bakkyaraj, T.; Sahadevan, R.: Invariant analysis of nonlinear fractional ordinary differential equations

#### Periodic boundary value problems for nth-order ordinary differential equations with p-laplacian

We prove existence results for solutions of periodic boundary value problems concerning the nth-order differential equation with p-Laplacian [φ(x(n−1)(t))] ... . Tsamatos , Solvability of an m-point boundary value problem for second order ordinary differential equations , J. Math. Anal. Appl . 189 ( 1995 ), no. 2 , 575 - 584 . [5] V. A. Il 'in and E. I. Mojseev

#### Periodic boundary value problem for second order integro-ordinary differential equations with general kernel and Carathéodory nonlinearities

We study the existence of solutions for the periodic boundary value problem for some second order integro-differential equations with a general kernel. Also we develop the monotone method to ... problem. - PERIODIC BOUNDARY VALUE PROBLEM FOR SECOND ORDER INTEGRO-ORDINARY DIFFERENTIAL EQUATIONS WITH GENERAL KERNEL AND CARATHIODORY NONLINEARITIES* (Received March 8, 1994 and in revised form

#### On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem

In the present paper we study nonlocal problems for ordinary differential equations with a discontinuous coefficient for the high order derivative. We establish sufficient conditions, known as ... Journal of Applied Mathematics and Stochastic Analysis ON NONLOCAL PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS AND ON A NONLOCAL PARABOLIC TRANSMISSION PROBLEM M. DENCHE 0 0 Universit de