Group Classification of a Family of Second-order Differential Equations
نویسنده
چکیده
We find the group of equivalence transformations for equations of the form y′′ = A(x)y′ +F(y), where A and F are arbitrary functions. We then give a complete group classification of these families of equations, using a direct method of analysis, together with the equivalence transformations.
منابع مشابه
Recurrent metrics in the geometry of second order differential equations
Given a pair (semispray $S$, metric $g$) on a tangent bundle, the family of nonlinear connections $N$ such that $g$ is recurrent with respect to $(S, N)$ with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair $(N, g)$ to be recurrent as well as for the triple $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$ is the canonical ...
متن کاملInitial value problems for second order hybrid fuzzy differential equations
Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia
متن کاملNumerical solution of second-order stochastic differential equations with Gaussian random parameters
In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...
متن کاملGeneralized H-differentiability for solving second order linear fuzzy differential equations
In this paper, a new approach for solving the second order fuzzy differential equations (FDE) with fuzzy initial value, under strongly generalized H-differentiability is presented. Solving first order fuzzy differential equations by extending 1-cut solution of the original problem and solving fuzzy integro-differential equations has been investigated by some authors (see for example cite{darabi...
متن کاملAnalytic Solution of Fuzzy Second Order Differential Equations under H-Derivation
In this paper, the solution of linear second order equations with fuzzy initialvalues are investigated. The analytic general solutions of them using a rstsolution is founded. The parametric form of fuzzy numbers to solve the secondorder equations is applied. The solutions are searched in four cases. Finallythe example is got to illustrate more and the solutions are shown in gures forfour cases.
متن کاملSymmetry group, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation
In this paper Lie point symmetries, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation are investigated. First of all Lie symmetries are obtained by using the general method based on invariance condition of a system of differential equations under a prolonged vector field. Then the structure of symmetry ...
متن کامل