Solve Initial Value Problem Differential Equations

The class of singular equations was generalized, by changing the coefficient of and the proposed technique was presented in a general way.

This gives the proposed scheme a wider applicability.

To illustrate the generalization discussed above, we discuss this example: Example 3. CONCLUSION In the discussion it was shown that, with the proper use of the taylor series method, it is possible to obtain an analytic solution to a class of singular initial value problems, homogeneous or inhomogeneous.

The difficulty in using a taylor series method directly to this type of equations, due to the existence of singular point at x = 0, is overcome here.

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].

1 for the function f (x, y) and the inhomogeneous term g (x).

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).

Most algorithms currently in use for handling the Lane-Emden-type problems are based on either series solution or perturbation techniques.

Wazwaz (2001) has given a general study to construct exact and series solution to Lane-Emden-type equations by employing the Adomian decomposition method.

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