Here we introduce the simplest linear, first-order ordinary differential equation, dx/dt = constant * x, using intuitive examples like the growth of a bunny population, radioactive decay, and compound interest in the bank. We solve this equation and find that the solutions are given by exponential functions in time. This is the basis for all of the differential equations in this series.

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This video was produced at the University of Washington

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0:58 Example: Bunny Population Growth
6:33 Solving this Differential Equation
15:03 What is Euler's Number 'e'? Example: Compound Interest
27:25 Loan Interest as a Differential Equation
31:23 Example: Radioactive Decay
36:32 Example: Thermal Runaway in Electronics