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ordinary differential
These oscillations and rotations of the satellite are described by an ordinary differential equation (Beletsky equation) of the second order with periodic coefficients and two parameters.
      
Using the maximum principle formalism, the problem of optimizing interorbital transfer between two noncoplanar elliptic orbits is reduced to solution of a boundary value problem for a system of ordinary differential equations.
      
The method we use is applicable to a wide class of nonlinear ordinary differential equations (ODEs) depending on parameters.
      
The position of the line of separation is determined from the solution of an ordinary differential equation.
      
However, the methods of solving the boundary layer equations in these studies are based on various simplifying assumptions which allow the problem to be reduced to the solution of a system of ordinary differential equations.
      
The objective of these assumptions is to reduce the boundary layer equations to ordinary differential equations.
      
The considered sequential approximation method for one-dimensional unsteady problems makes it possible to reduce the solution to the integration of systems of ordinary differential equations.
      
Since the characteristic dimension is missing in this problem, the problem is self-similar and, consequently, reduces to the solution of ordinary differential equations.
      
The basic integral equation for determining the vortex distribution density is reduced to the Abel equation by solving an auxiliary system of ordinary differential equations.
      
In the following we determine the law of shock-front motion in this problem via the method of [1], which makes it possible to find a system of ordinary differential equations for the problem.
      
Using a finite integral Hankel transform, the problem is reduced to the solution of a system of ordinary differential equations.
      
Under determined conditions, the problem is found to be self-similar, and comes down to the solution of a system of ordinary differential equations.
      
The Lyapunov-Schmidt method is used [1, 2]; the boundary-value problems for ordinary differential equations arising in the case of its realization are solved numerically on a computer.
      
In the given mathematical model of turbulence (in contrast to other models of finite dimensions), the accurate hydrodynamic equation is not replaced by a finite system of coupled ordinary differential equations, and singular initial data are used.
      
An ordinary differential equation of the second order is derived for the function in terms of which the stress and other characteristics of the crust are expressed.
      
A system of ordinary differential equations is derived for finding the transverse force and moment.
      
The investigation reduces to a study of a system of nonlinear ordinary differential equations.
      
With such an approach the problem is reduced to finding the solutions to ordinary differential equations with variable coefficients which depend on the parameter λ.
      
The equations reduce to a system of ordinary differential equations, which are solved numerically by the orthogonal sweep method [1].
      
A statistical analysis is made of random nonlinear plane waves in a gas with polytropic exponent γ = 3 by reduction of the original problem to an auxiliary Cauchy boundary-value problem for a system of stochastic ordinary differential equations.
      
 

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