Separation of Variables (Edexcel International A Level (IAL) Maths): Revision Note

Separation of variables

What does it mean for a differential equation to be separable?

• Many differential equations used in modelling have two variables involved (ie x and y)

• If there is a product of functions in different variables, the differential equation is separable

  • ie dy/dx = f(x) × g(y)

• Differential equations of the form dy/dx= g(y) should be though t of as dy/dx= 1 × g(y)

  • where f(x) = 1

How do I solve a differential equation using separation of variables?

• 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