How do I solve a differential equation?
- Solving differential equations uses integration!
- The precise integration method will depend on the type of question (see Decision Making)
- Separation of variables is highly likely to be involved
- Particular solutions are usually required to Differential Equations
- An initial/boundary condition is needed
- Solutions can be rewritten in a format relevant to the model
- The solution can be used to make predictions at other times
- Temperature after four minutes
- Volume of sales after another three months
How do I use the solution to a differential equation?
- Questions may ask you to interpret your solutions in the context of the problem
- There could be links to other areas of A level maths – such as mechanics
- Sometimes multiple rates of change may be involved in a model or problem
- See Connected Rates of Change
How do I interpret a differential equation?
- Models may not always be realistic in the long term
- A population will not grow indefinitely – it will reach a natural limit
- You will be expected to interpret and comment on the model