OCR A Level Maths: Pure

Revision Notes

8.3.3 Separation of Variables

Separation of Variables

What does separation of variables mean?

-Notes-sv_eg, AS & A Level Maths revision notes

  • Many differential equations used in modelling either …
    • … have two variables involved (ie x and y), or,
    • ... involve a function of the dependent variable (ie y) only

  • This is particularly true where proportionality is involved
    • eg population change is dependent on both time and the size of the population

8.3.3 Notes sv_eg2, AS & A Level Maths revision notes

 

  • This type of question is covered in more detail in Modelling with Differential Equations

How do I know if I need to separate the variable in a question?

Notes sv_eg_dydx, AS & A Level Maths revision notes

 

  • There is a product of functions in different variables
    • ie dy/dx = f(x) × g(y)

  • It will not be possible to integrate directly from an equation in the form dy/dx= g(y)

How do I solve a separating variables question?

8-3-3-notes-sv-eg-soltn

  • STEP 1: Separate all y terms on one side and all x terms on the other side
  • STEP 2: Integrate both sides
  • STEP 3: Include one “overall” constant of integration
  • STEP 4: Use the initial or boundary condition to find the particular solution
  • STEP 5: Write the particular solution in sensible, or required, format

Worked example

Example soltn, AS & A Level Maths revision notes

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Paul

Author: Paul

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.