Solution and Analysis of System of Differential Equation with Initial Condition as �

In this present study, we have analyzed the solution of system of first order simultaneous differential equations with initial condition as a neutrosophic environment. Here, we consider the initial values as Trapezoidal Neutrosophic Numbers (). The solution procedure of the system of first order ODE is developed using and (, , ) of a . Furthermore, a numerical example is illustrated to validate the efficiency and feasibility of the proposed neutrosophic method, and the solutions are compared with the crisp values. The numerical solutions 1 (, ), 2 (, ), 1 ′ (, ), 2 ′ (, ), 1 ′′(, ), 2 ′′(, ), 1 (, ), 2 (, ), 1 ′ (, ), 2 ′ (, ), 1 ′′(, ) 2 ′′(, ) for the different values of , and at = 0.5 are examined via tables and graphs. The numerical solutions delight the conditions of strong solution