Solve Initial Value Problem Differential Equations

Equation 1 with specializing f (y) was used to model several phenomena in mathematical Physics and astrophysics such as the theory of stellar structure, the thermal behavior of a spherical cloud of gas, isothermal gas spheres and theory of thermionic currents Chandrasekhar (1976) and Davis (1962).We consider the new auxiliary (nonhomogeneous, but easily solvable) (4) instead of (42).The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases.We are interested in the existence of solutions to initial-value problems for second-order nonlinear singular differential equations.We show that the existence of a solution can be explained in terms of a more simple initial-value problem.The approach used here can be useful for the problems on the existence of solutions of boundary value problems [23–26].The authors in [23, 24] established remarkable theorems on the existence and uniqueness of the solution of the equation Our approach is different from the approach in [23–25].Moreover, a generalization was developed in Wazwaz (2001) by replacing the coefficient 2/x of (x) by n/x. It is important to note that (2), with boundary conditions, has attracted many mathematicians and has been studied from various points of view. Singular initial value problems, linear and nonlinear, homogeneous and nonhomogeneous, are investigated by using Taylor series method. One of the equations describing this type is the Lane-Emden-type equations formulated as.The solutions are constructed in the form of a convergent series. where A and B are constants, f (x, y) is a continuous real valued function and g (x) ∈ c [0,1].

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