The second-order linear homogeneous differential equations in differential equation theory occupies an important position, but the second order differential equation has no general solution method, most of the solutions of these equations is difficult to obtain analytical expressions and even some impossible to obtain the solution of the form, and the second order differential equation solving is divided into homogeneous and inhomogeneous problems.

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First of all,we have given some of the basic concepts of differential equations, described the constant coefficient linear ordinary differential equation solution, for a class of second-order variable coefficient linear ordinary differential equation initial value problem, an approximate solution, the method is first unknown function of a definition for N sub-interval, and then in between each district within a constant coefficient ordinary differential equations similar to the replacement, the solution has been the problem as similar to the original analytical solution, and then gives a detailed second-order change order coefficient of linear homogeneous ordinary differential equation solution examples, the examples of the approximate method proposed in this paper is valid.

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This article uses the step-by-step Fourier method and normalized NLSE was solved, and analog input for the first-order,second-order and third-order hyperbolic secant optical pulses under the conditions of the evolution of optical pulse transmission.

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The construction of the international shipping center, besides offering advanced hardware facilities, the soft environment of the high-quality, high-efficient, security is the condition that an international shipping center must possess too, and the good water traffic safety order is an extremely important condition of soft environment in an international shipping center construction, in order to adapt to the construction of the international shipping center of Shanghai, port unit like customs , frontier unit put into a large amount of manpower and materials and the soft environmental constructions related to international shipping center in succession, meanwhile, to ensure the work to put forward the new request of Shanghai Maritime Affairs Bureau who is responsible for Shanghai harbor water traffic safety supervision management and boat policy management, in order to adapt to the construction of fast-developing international shipping center of Shanghai, it is immanency to research and construct and implement of boat policy to develop the high-capacity and high-technology patrol ships.

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A logical product structure model was constructed which can describe the infinite product variants,and support to solve product configuration under the mixed environment of Assemble-to-Order and Make-to-Order. In order to be identified and managed ,Logical product structure model was described with the knowledge representation method based on production rule.Finally the feasibility of the method was confirmed by simulation of a simplification automobile product family.

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These constructional methods can be used to treat many problems, the numerical results show that the given interval extension has smaller excessive width relative to the range of the functions over a domain. For univariate differentiable functions, the definition of interval slope is extended from the first order to high order according to their differentiability, and iterative formula of high-order interval slope computation is also developed.

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This time the universal time is on August 1, 2999 in the afternoon 2.15 minutes, Huang Qu senior official yellow Jinlong, already led his interplanetary flight group to compel always to raid the planetoid rapidly, in order to arrive personally the first front not to disrupt the whole plan deployment, he the 12th group's jointure of command for vice-group leader Commander Ms. Diana, then, led several guard starship, the acceleration to rush immediately the first interspace group nearby air zone, in order to nearby examine the special details, and prepared to land ahead of time this planetoid, in order to could direct other interspace group debarkation immediately and launch fast pulls out the spatial planetoid the ultimate fight.

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Based on Fermat's theorem, the law of reflection and refraction is obtained, and the geometrical ray tracing method of reflected light is introduced. In response to geometric optics rainbow theory and Airy rainbow theory, the relationship formula of the N-order rainbow angle with the refraction index and the Airy peak value position formula are derived, and the physics causation of the first order rainbow are discussed and analyzed in detail. The distribution properties of the first and second order Airy structures of spherical particles are calculated.

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For the compressible materials, in order to satisfy the higher-order compatibility equation of the rate of deformation in the centered fan sector, which is a quite difficult problem unresolved in the previous studies, a particular term must be added to the expansions of the stress components in the regular logarithmic power series adopted by many researchers before. A higher-order near tip field with tangential velocity jump ahead of the crack tip is derived first, of which the dominant terms are the solution widely accepted.

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