Following completion of this free OpenLearn course, Introduction to differential equations, as well as being able to solve first-order differential equations you should find that you are increasingly able to communicate mathematical ideas and apply your knowledge and understanding to mathematics in everyday life, in particular to applications such as population models and radioactive decay.
You should now be able to:
- recognise differential equations that can be solved by each of the three methods, direct integration, separation of variables and integrating factor method, and to 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.
This free OpenLearn course is an extract from the Open University module MST124 Essential mathematics 1. If you feel you are ready to move on but don’t have time to study a full Open University module at this time, you might like to study the free OpenLearn course, Introduction to number theory, another adapted extract from the Open University module, MST125 Essential mathematics 2. If you are interested in statistics you may like to study the free OpenLearn course, Prices, location & spread, an adapted extract from the Open University module M140 Introducing statistics.. To see if you are ready to study MST125, click on the link and follow the ‘Am I ready?’ advice in the module description, and/or to refresh your knowledge of related mathematical topics consider