This paper primarily introduces the Euler technique and the fourth-order Runge Kutta technique (RK4) as algorithms for solving Initial Value Problems (IVP) in the context of ordinary differential equations (ODE). The two proposed solutions exhibit a high level of efficiency and practical suitability in addressing these difficulties. To ascertain the accuracy, a comparison is made between numerical solutions and exact solutions. The obtained numerical solutions exhibit a high level of concordance with the exact solutions. Comparative analysis has been conducted to evaluate the numerical performance of the Euler method and the Runge-Kutta method. For the purpose of attaining enhanced precision in the solution, it is important to minimise the step size. In conclusion, we conduct an investigation and calculate the mistakes associated with the two proposed approaches for a specific single step size in order to assess their relative superiority.