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AQA A Level Maths: Pure復(fù)習(xí)筆記8.3.1 General Solutions

Category: A-level課程, 教材筆記, 福利干貨 Date: 2022年8月9日 上午11:43

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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