General Solutions (Edexcel International A Level (IAL) Maths) : Revision Note

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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 Content Creator (Previous)

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.

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