CIE A Level Maths: Pure 3復習筆記5.2.1 General Solutions
General Solutions
What is a differential equation?
- 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?
- 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
Worked Example
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