Comparison of solving differential equation in a continuous simulation

Introduction

In a quasi-continuous simulation, numerical methods for solving differential equations are used. So the chosen methods are:

Algorithm	Description
Euler method	one-step method
Runge-Kutta method	multi-step method

The solved differential equation

$$y(x) = c_1 \cdot e^{x} + x^{3} + 3x^{2} + 6x + 6,$$ where $c_{1}=1$

The function

$$\frac{dy}{dx} = y-x^{3}$$

Result

Red curve - Real values
Blue curve - Eulier values
Black curve - RK4 value