Sentence examples for particular solution of the from inspiring English sources

To illustrate the method, suppose it is desired to find a particular solution of the equation y″ + p(x y′ + q(x y = g(x).To use this method, it is necessary first to know the general solution of the corresponding homogeneous equation i.e., the related equation in which the right-hand side is zero.

In particular, solution of the lower concentration is easily recrystallized.

which proves that is a particular solution of the inhomogeneous Kummer's equation (1.4).

Therefore, x ∗ is a particular solution of the variational inequality (3.1).

which proves that is a particular solution of the inhomogeneous equation (1.8).

We show that the sequence x n defined by (3.2) converges to a particular solution of the variational inequality (3.1).

Then, the multiquadric and polynomial particular solutions of the biharmonic equation are obtained respectively by straight integrations and referring to the first author's recent study.

Periodic vibrations are described by particular solutions of the equations of motion, resulting from trigonometric expansions of sequences of Dirac distributions.

In fluid dynamical problems the main questions treated are the study of exact or particular solutions of the PDE approximations – called Prandtl's equations – to the Navier Stokes equations.

where q j p (t) and p j p (t) are classical particular solutions of the firstly transformed system described by Ĥ A in the charge and the current spaces, respectively.

The purpose of this paper is to present a certain class of the explicit particular solutions of the associated Cauchy-Euler fractional partial differential equation of arbitrary real or complex orders and their applications as follows: where u = u ( x, t ) ; A, B, C, M, N, α and β are arbitrary constants.