Linear differential equation


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(Math.) an equation which is of the first degree, when the expression which is equated to zero is regarded as a function of the dependent variable and its differential coefficients.

See also: Linear

References in periodicals archive ?
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 equation
These 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.
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