Differential equations
Write a rate of change as a differential equation, find the solution y = Cekx on a graph and solve a separable equation with a starting condition.
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Guide
A differential equation links a rate of change to the quantity itself. "The rate of growth is proportional to the amount" means dPdt = kP. A decrease is written with a minus sign.
The solution of a differential equation is a function, not a number: a family of graphs with a constant C. A starting condition (for example y = 2 when x = 0) picks one of them.
For a separable equation, put y and dy on one side and x and dx on the other, integrate both sides and write the C straight away.