Separation of Variables (OCR A Level Maths A) : Revision Note

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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

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