CIE A Level Maths: Pure 3复习笔记5.2.1 General Solutions

General Solutions

What is a differential equation?

8.3.1-Notes-des_egs

  • 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?

8.3.1-Notes-des_gen_sol

  • 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

    8.3.1-Notes-des_geb_sol_eg

Worked Example

8.3.1-Example-soltn

 

 

 

 

 

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