A LevelMaths: Pure 3CIERevision Notes5. Integration5.2 Differential Equations5.2.1 General Solutions

General Solutions (CIE A Level Maths: Pure 3)

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General Solutions

What is a differential equation?

Notes des_egs, AS & A Level Maths revision notes

  • Any equation, involving a derivative term, is a differential equation
  • Equations involving only first derivative terms are called first order differential equations
  • Equations involving second derivative terms are called second order differential equations

What is a general solution?

Notes des_gen_sol, AS & A Level Maths revision notes

  • Integration will be involved in solving the differential equation
    • ie working back to “y = f(x)”

  • A constant of integration, c is produced
  • This gives an infinite number of solutions to the differential equation, each of the form y = g(x) + c  (ie  y = f(x)  where  f(x) = g(x) + c)
  • These are often called a family of solutions …
    • … and the solution y= g(x) + c is called the general solution

     Notes des_geb_sol_eg, AS & A Level Maths revision notes

Worked example

Example soltn, 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.