Particular Solutions (CIE A Level Maths: Pure 3)

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Particular Solutions

What is a particular solution?

  • Ensure you are familiar with General Solutions first
  • With extra information, the constant of integration, c, can be found
  • This means the particular solution (from the family of solutions) can be found

 Notes ps_eg, AS & A Level Maths revision notes

What is a boundary condition/initial condition?

  • A boundary condition is a piece of extra information that lets you find the particular solution
    • For example knowing y = 4 when x = 0 in the preceding example
    • In a model this could be a particle coming to rest after a certain time, ie v = 0 at time t

Notes ps_bound_cond, AS & A Level Maths revision notes

  • Differential equations are used in modelling, experiments and real-life situations
  • A boundary condition is often called an initial condition when it gives the situation at the start of the model or experiment
    • This is often linked to time, so t = 0

Notes ps_init_cond, AS & A Level Maths revision notes 

  • It is possible to have two boundary conditions
    • eg a particle initially at rest has velocity, v = 0 and acceleration, a = 0 at time, t = 0
    • for a second order differential equation you need two boundary conditions to find the particular solution

Worked example

Example soltn_a, AS & A Level Maths revision notesExample soltn_b, 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.