First-order linear inhomogeneous differential

The First-Order Linear Inhomogeneous Differential Equation (FOLIDE) First-Order Reaction Including Back Reaction Reaction of Higher Order Catalyzed Reactions... 

In Eqs. 12-47/48 we recognize the first-order linear inhomogeneous differential equation (FOLIDE, Box 12.1). Depending on whether the input I and the different rate constants (kw, kj) are constant with time, their solutions are given in Eqs. 6,8, or 9 of Box 12.1. 

Box21.6 Solution of Two Coupled First-Order Linear Inhomogeneous Differential Equations (Coupled FOLIDEs)... 

Equation (4.11) is an inhomogeneous first-order linear differential equation of a t). By multiplying both sides of Eq. (4.11) by an integration factor exp(t/r), the Maxwell equation can be easily transformed into the integration form... 

Equation (6.57) is an inhomogeneous first-order linear differential equation of the tensor X[oj in the range —oo < t < t. With the condition that X[o] is finite at t = —oo, we may obtain the solution for X[oj. X[oj(t,t) = x(i), as the convected coordinates coincide with the fixed coordinates when... 

Thus we are confronted with the solution of a two-point boundary value problem for a linear system of first order differential equations. In the event that the rod is inhomogeneous, the matrices A, , (7, or D will depend on y. 

The model of isotope transfer in CSTR is a set of ordinary inhomogeneous differential equations with linear right side, which are solved by standard methods of expansion into eigenvectors. With the known eigenvalues and eigenvectors, it is easy to calculate first- and second-order derivatives, which makes the minimization procedure much faster. 

We present a brief introduction to coupled transport processes described macroscopically by hydrodynamic equations, the Navier-Stokes equations [4]. These are difficult, highly non-linear coupled partial differential equations they are frequently approximated. One such approximation consists of the Lorenz equations [5,6], which are obtained from the Navier-Stokes equations by Fourier transform of the spatial variables in those equations, retention of first order Fourier modes and restriction to small deviations from a bifurcation of an homogeneous motionless stationary state (a conductive state) to an inhomogeneous convective state in Rayleigh-Benard convection (see the next paragraph). The Lorenz equations have been applied successfully in various fields ranging from meteorology to laser physics. 

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