Topic 6: Rates of Change and Differential Equations

2 dot points, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

How do we solve a differential equation by separating the two variables onto opposite sides?

Solve first-order separable differential equations and find particular solutions using initial conditions.

Solving first-order separable differential equations by separating variables and integrating both sides, applying initial conditions to find the particular solution, and handling the constant of integration.

8 min read →

How do we translate a real situation into a differential equation and interpret its solution?

Formulate and solve differential equations modelling real situations such as growth, cooling and limited growth, and interpret the solutions.

Setting up differential equations from worded situations including exponential growth and decay, Newton's law of cooling and logistic limited growth, solving them, and interpreting the long-term behaviour.

9 min read →