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A differential equation relates a function to its rate of change. This topic forms and solves first-order differential equations by separating the variables and integrating, applied to growth and decay. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Separate the variables so each side involves only one letter, then integrate both sides, putting the constant on one side only. Use the initial condition to find that constant, then rearrange into the form the question asks for.
Before you start
This builds directly on integration and separation of variables. Examined in Pure 4. Getting it right here pays off in modelling growth, decay and rates. The topic sits within Integration.
What you learn
Separate first, then choose the right integration method for each side. Translate a described rate into a differential equation, solve it, and use conditions to answer the question — the core of exam modelling. The course works through separating the variables, the particular solution, exponential growth & decay, harder separable equations and modelling with differential equations. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Differential Equations is part of the Integration strand of our free A-level maths courses, studied in the second year of A-level. There are 5 teaching sections and 5 fully worked examples, plus 5 sets of check questions. Nearby topics in the same strand are Indefinite Integrals, Integration by Parts, Integration by Substitution, Integration of f(ax+b) and Integration of Standard Functions. Endless extra practice on this strand is available on the Integration revision engine, which generates a fresh question each time.
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