Given

system of ordinary differential equation is By Applying Aboodh transformation method

Then a linear

system of ordinary differential equation is obtained.

The model was formulated as a

system of ordinary differential equations (ODEs) and as a Petri Net (PN) - the PN is a graphical based model which is useful in identifying critical perturbations within biological reaction networks and the ODEs can give quantitative information e.g.

The direct approach is useful for scalar ordinary differential equations only but does not work for

system of ordinary differential equations [6].

Reference [15] established a new iteration improvement of the solution based on the dynamic

system of ordinary differential equations (ODEs), and the new method is more effective than Wilkinson's method.

Numerical solution of

system of ordinary differential equations with tau method: An error analysis.Math.

(2011) that with the physical parameters the system of partial differential equations could be replaced by a

system of ordinary differential equations because both systems gave identical results.

These Lie point symmetries are then used to transform the system (2a) and (2b) to a

system of ordinary differential equations (ODEs).

Considering

system of ordinary differential equations (4), we have

The first step leads to a

system of ordinary differential equations. This allows the use of a numerical technology and software specialized for the integration in [t.sup.*], which appears as a continuous variable in the

system of ordinary differential equations (Cash, 2005).

We derive some sufficient conditions for the existence of certain class of solutions of a second order partial differential equation (PDE) based on the hypothesis of Lie's theorem on fundamental set of solutions of a

system of ordinary differential equations. Then, we establish some necessary and sufficient conditions where a certain PDE is compatible with differential constraints of second order.

Another important mathematical modeling problem in physical metrology is fitting a

system of ordinary differential equations (ODEs) to a set of observed time series data which are corrupted by measurement errors.