IB DP Maths: AA HL复习笔记5.10.2 Analytical Solutions to Differential Equations
Separation of Variables
What is separation of variables?
- Separation of variables can be used to solve certain types of first order differential equations
If the equation is in that form you can use separation of variables to try to solve it- If the equation is not in that form you will need to use another solution method
How do I solve a differential equation using separation of variables?
Exam Tip
Worked Example
Homogeneous Differential Equations
What is a homogeneous first order differential equation?
How do I solve a homogeneous first order differential equation?
What else should I know about solving homogeneous first order differential equations?
Exam Tip
- Unless the question asks for it, you don’t have to change your solution into y = f(x) form – sometimes it might be more convenient to leave your solution in another form
Worked Example
Integrating Factor
What is an integrating factor?
How do I use an integrating factor to solve a differential equation?
What else should I know about using an integrating factor to solve differential equations?
- After finding the general solution using the steps above you may be asked to do other things with the solution
- For example you may be asked to find the solution corresponding to certain initial or boundary conditions
Worked Example
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