APPLICATION OF FIRST ORDER DIFFERENTIAL EQUATION IN REAL LIFE

If the roots of the algebraic equation are not distinct then we will not obtain all the solutions of the differential equation. Suppose that λ 1 = α is a double root. We substitute y = e λx into the differential equation.
L[e λx ] = [(λ − α) 2 (λ −[r]

( t − s ) p − 1 x ( s ) ds
⎞
⎠ , τ 0 ≤ t ≤ T (2 : 1 : 2)
respectively order of 0 < q < 1, and p + q = 1 where Γ denotes the Gamma function. Fractional derivatives and integrals play an important role in the development of the- ory of fractional dynamic[r]

Recently, Yang and Wei 23 and the author of 24 improved and generalized the results of Pang et al. 22 by using di ff erent methods, respectively.
On the other hand, it is well known that fixed point theorem of cone expansion and compression of norm type has been ap[r]

Thermal Transitions on Cooling of Rice Starch 38
1. INTRODUCTION
Differential scanning calorimetry (DSC) is a technique commonly employed to probe thermal properties of starch based on the heat[r]

For visualization, the main stages of constructing generalized separable solutions by the splitting method are displayed in Fig. 15.2.
15.5.4-2. Solutions of simple functional equations and their application.
Below we give solutions to two simple bilinear functional e[r]

in Theorem 3.1 , so, we do not need to suppose that G t, s is nonnegative.
Remark 3.3. The function f in Theorem 3.1 is not monotone or convex; the conclusions and the proof used in this paper are di ff erent from the known papers in essence.
Proof. It is easy to see[r]

We consider the static deflection of an infinite beam resting on a nonlinear and non-uniform elastic foundation. The governing equation is a fourth-order nonlinear ordinary differential equation. Using the Green’s function for the well-analyzed linear version [r]

Xem Thêm " NONLINEAR STABILITY ANALYSIS OF ECCENTRICALLY STIFFENED S-FGM IMPERFECT PLATES RESTING ON ELASTIC FOUNDATIONS "

Xem Thêm " FINITE-DIFFERENCE METHOD FOR THE GAMMA EQUATION ON NON-UNIFORM GRIDS "

This chapter discusses the following topics. In section 2 we motivate MOC by applying it to a first-order scalar hyperbolic equation. It is useful to understand this problem because it is an essential component when studying certain classes of two-factor models [r]

5. Van, TD, Tsuji, M, Thai Son, ND: The Characteristics method and Its Generalizations for First Order Nonlinear Partial Differential equations. Chapmann and Hall/CRC, Boca Raton, FL (2000)
6. Brandi, P, Marcelli, C: Haar Inequality in hereditary setting and application[r]

14.3.1-1. Preliminary remarks.
For brevity, in this paragraph a homogeneous linear partial differential equation will be written as
L [ w ] = 0 . (14. 3 . 1 . 1 ) For second-order linear parabolic and hyperbolic equations, the linear differential opera- tor L [[r]

4 4 4 4
In the last section we looked at a frictionless model of a vibrating spring from the perspective of a system of differential equations. We sketched solution curves in the position-velocity phase-plane, but we did not nd position as a function of[r]

4 4 4 4
In the last section we looked at a frictionless model of a vibrating spring from the perspective of a system of differential equations. We sketched solution curves in the position-velocity phase-plane, but we did not nd position as a function of[r]

The unique photophysical properties of the Ln(III) series has led to significant research efforts being directed towards
their application in sensors. However, for “real-life” applications, these sensors should ideally be immobilised onto surfaces without loss of function.

November 19, 2001 Abstract
A model of shallow fluid behavior is evaluated using a variety of nu- merical solving techniques. The model is defined by a pair of partial dif- ferential equations which have two dimensions in space and one dimension of time. The equat[r]

obtain the form of the desired solution, w = | x | c/a Ψ y | x | – b/a
, where Ψ (z) is an unknown function.
To make it clearer, the general scheme for constructing invariant solutions for evolution second-order equations is depicted in Fig. 15.4. The first-order[r]

138 Laxminarayan, Singh, Suri
3.7.3 Conclusions and the Future on Level Sets
The class of differential geometry, also called level sets, has been shown to dominate medical imaging in a major way. There is still a need to under- stand how regularization terms can be[r]

This book provides context and structure for learning the fundamental principles of organic chemistry, enabling the reader to proceed from simple to complex examples in a systematic and logical way.
(BQ) Part 1 book Partial differential equations in action has contents: Introduction, diffusion, the[r]

(1)
in which the function y ( x ) is to be found.
In order to apply the Fourier transform technique (see Subsections 7.4-3, 10.4-1, and 10.4-2), we extend the domain of both conditions in Eq. (1) by formally rewriting them for all real values of x[r]

(BQ) Part 1 book Partial differential equations in action has contents: Introduction, diffusion, the laplace equation, scalar conservation laws and first order equations, waves and vibrations.

(BQ) Part 1 book Partial differential equations in action has contents: Introduction, diffusion, the lapla[r]

control the particular type and order of the solution of the Bessel equation which is described in the volume ‘The series solution of second order, ordinary differential equations and sp[r]