Explore the fundamentals of linear, first-order ordinary differential equations in this 39-minute video lecture. Delve into intuitive examples such as bunny population growth, radioactive decay, and compound interest to understand the equation dx/dt = constant * x. Learn how to solve this equation and discover that solutions are given by exponential functions in time. Gain insights into Euler's number 'e' and its significance in compound interest calculations. Examine practical applications including loan interest, radioactive decay, and thermal runaway in electronics. This lecture serves as a foundation for more complex differential equations, providing a comprehensive introduction to the topic with real-world examples and clear explanations.