AQA A Level Maths: Pure复习笔记8.3.5 Solving & Interpreting Differential Equations

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

    8.3.5-Notes-de_solve

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

8.3.5-Notes-de_exp_and_A

  • 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

8.3.5-Notes-de_solve_and_use_qu

8.3.5-Notes-de_solve_and_use

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

8.3.5-Notes-de_solve_mechs_qu

8.3.5-Notes-de_solve_mechs

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

8.3.5-Notes-de_croc_solve1

8.3.5-Notes-de_croc_solve2

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

8.3.5-Notes-desolve_and_limit

Worked Example

8.3.5-Example-soltn18.3.5-Example-soltn2

 

 

 

 

 

 

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