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Separation of Variables (CIE A Level Maths: Pure 3)
Revision Note
Separation of Variables
What does separation of variables mean?
- Many differential equations used in modelling either …
- … have two variables involved (ie x and y), or,
- ... involve a function of the dependent variable (ie y) only
- This is particularly true where proportionality is involved
- eg population change is dependent on both time and the size of the population
- This type of question is covered in more detail in Modelling with Differential Equations
How do I know if I need to separate the variable in a question?
- There is a product of functions in different variables
- ie dy/dx = f(x) × g(y)
- It will not be possible to integrate directly from an equation in the form dy/dx= g(y)
How do I solve a separating variables question?
- STEP 1: Separate all y terms on one side and all x terms on the other side
- STEP 2: Integrate both sides
- STEP 3: Include one “overall” constant of integration
- STEP 4: Use the initial or boundary condition to find the particular solution
- STEP 5: Write the particular solution in sensible, or required, format
Worked example
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