Solving & Interpreting Differential Equations (CIE A Level Maths: Pure 3)

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Solving & Interpreting Differential Equations

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

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  • Solutions can be rewritten in a format relevant to the model

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  • 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

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Notes de_solve_and_use, AS & A Level Maths revision notes

  • There could be links to other areas of A level maths – such as mechanics

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  • Sometimes multiple rates of change may be involved in a model or problem
    • See Connected Rates of Change

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Notes de_croc_solve2, AS & A Level Maths revision notes

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

Notes de+solve_and_limit, AS & A Level Maths revision notes

Worked example

Example soltn1, AS & A Level Maths revision notesExample soltn2, AS & A Level Maths revision notes

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.