Solving & Interpreting Differential Equations (Edexcel IAL Maths)

Spec point — 6.4

Solving & interpreting differential equations

How do I solve a differential equation from a given model?

• Solving differential equations from a given model using the same techniques as before, for example separation of variables

• The precise integration method will depend on the type of question (see Decision Making)

• 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 can I use the solution of a differential equation to answer modelling questions?

• 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 can I interpret a model using the solution to the 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

Worked Example