Calculus › Section G · Differential equations › Topic G.3
Separation of variables
Growth and decay solved one special equation, y′ = ky. Separation of variables solves a whole family of equations, including cooling, mixing and geometry problems, by turning each into two ordinary integrals.
In this topic
- The easy equation, and everything else
- What separable means
- The method: separate, integrate, solve
- Worked example: y′ = 2xy with an initial condition
- Worked example: y′ = −x/y and implicit solutions
- Solutions lost by dividing
- Newton's law of cooling, solved
- A flushing tank
- Orthogonal trajectories
- When solutions blow up
- Common mistakes to avoid
- Key takeaways
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Standards: 7