Differential equations are any equations that include derivatives and arise in many situations. This free course, Introduction to differential equations, considers three types of first-order differential equations.

Learning outcomes:

• Recognise differential equations that can be solved by each of the three methods – direct integration, separation of variables and integrating factor method – and use the appropriate method to solve them.
• Use an initial condition to find a particular solution of a differential equation, given a general solution.
• Check a solution of a differential equation in explicit or implicit form, by substituting it into the differential equation.
• Understand the terms ‘exponential growth/decay’, ‘proportionate growth rate’ and ‘doubling/halving time’ when applied to population models, and the terms ‘exponential decay’, ‘decay constant’ and ‘half-life’ when applied to radioactivity.
• Solve problems involving exponential growth and decay.