Differential equation in python - Simple ODE using Python and SciPy

In this video, we explore how to solve a simple Ordinary Differential Equation (ODE) using Python and the SciPy library. The specific ODE we tackle is a first-order linear ODE representing exponential decay. The equation is given by dy/dt = -k * y, where y is the dependent variable, t is time, and k is a constant.

Key Points:
1. Introduction to Ordinary Differential Equations (ODEs) and their applications.
2. Overview of the exponential decay ODE: dy/dt = -k * y.
3. Demonstration of coding the ODE using Python and the SciPy library.
4. Setting up the initial conditions and time span for simulation.
5. Integration of the ODE using SciPy's odeint function.
6. Visualization of the numerical solution alongside the exact solution.
7. Comparison of the numerical solution with the analytical solution.
8. Discussion on the impact of the decay constant (k) on the solution.
9. Insights into the behavior of exponential decay over time.
10. Conclusion and summary of key learnings.

By the end of this video, you'll have a clear understanding of how to use Python and SciPy to solve simple ODEs, with a focus on the exponential decay model. This knowledge can be applied to various fields, including physics, chemistry, biology, and engineering. Don't forget to like, subscribe, and hit the notification bell for more content on numerical simulations and scientific computing with Python!