Therefore, the problem mapped onto the new domain is not of the form of Poisson's equation but a little more complex two-variable second-order

linear differential equation, which requires the solution introduced in Section 2.

XI] has generalized the classical Lyapunov inequality for the

linear differential equationThese polynomials, called Freud-type orthogonal polynomials, satisfy a second order

linear differential equation with varying polynomial coefficients.

Unfortunately, not every non

linear differential equation has a small parameter.

It is well known that the corresponding Caratheodory function satisfies a first order

linear differential equation[15] Walter Leighton, The detection of the oscillation of solutions of a second order

linear differential equation, Duke Math.

Section 2 discussed the oscillatory and nonoscillatory properties of the third-order

linear differential equation. In Section 3, the necessary conditions and the derivation for exponentially fitted and trigonometrically fitted modified Runge-Kutta type methods for solving third-order ODEs are given.

Ra[section]a, "On the Hyers-Ulam stability of the

linear differential equation," Journal of Mathematical Analysis and Applications, vol.

In this paper we consider the scalar

linear differential equation with time varying delay

The first of them is a

linear differential equation with coefficients depending on time (4).

In the value distribution theory of entire functions, Bruck's conjecture [6] is still an open question, and it has close relation to the following nonhomogeneous complex

linear differential equation,

[6] obtained the Hyers-Ulam stability of a

linear differential equation using Laplace transforms.