A theorem on energy integrals for linear second-order ordinary differential equations with variable coefficients

Remarks on Invariant Method of the Second-Order Linear Differential Equations with Variable Coefficients

Singular Eigenvalue Problems for Second Order Linear Ordinary Differential Equations

We consider linear differential equations of the form (p(t)x′)′ + λq(t)x = 0 (p(t) > 0, q(t) > 0) (A) on an infinite interval [a,∞) and study the problem of finding those values of λ for which (A) has principal solutions x0(t;λ) vanishing at t = a. This problem may well be called a singular eigenvalue problem, since requiring x0(t;λ) to be a principal solution can be considered as a boundary co...

Formulas for Solution of the Linear Differential Equations of the Second Order with the Variable Coefficients

Received: January 10, 2011 Accepted: February 10, 2011 doi:10.5539/jmr.v3n3p32 Abstract In this paper we obtained the formula for the common solution of the linear differential equation of the second order with the variable coefficients in the more common case. We also obtained the formula for the solution of the Cauchy problem.

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

Discrete Galerkin Method for Higher Even-Order Integro-Differential Equations with Variable Coefficients

This paper presents discrete Galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. We use the generalized Jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. Numerical results are presented to demonstrate the effectiven...