This paper proposes a new minimization technique for of the solutions of differential equation using non-linear Nelder-Mead Simplex algorithm and compare with genetic algorithm. We have solved differential problems both with Nelder-Mead simplex and genetic algorithm. The designed differential equation has been calculated as an error function for the minimization process. The proposed procedure has the capability to minimize the obtained solutions through any numerical techniques. The effectiveness of the proposed techniques guarantees the minimization of nonlinear differential equation with initial conditions. The resultant technique has a global validity for the minimization of differential equation. Genetic algorithm (GA) is suggested to minimize the differential problem, accessible to show the performance of the GA. Numerical outcomes obtained using Nelder-Mead Simplex guarantees its effectiveness.