Separation of variables (differential equations)

Separation of variables is a technique for solving a first order ordinary differential equation of the form

𝑑 𝑦 𝑑 𝑥 = 𝐹 (𝑥) 𝐺 (𝑦)

which can be solved by separating the $𝑥$ and $𝑦$ terms

\int 𝐹 (𝑥) 𝑑 𝑥 - \int 𝑑 𝑦 𝐺 (𝑦)

An ODE which can be solved this way is called separable.

Practice problems

2017. Elementary differential equations and boundary value problems, p. 38 (§2.2 problems)
2016. Calculus, pp. 645–648 (§9.3 exercises)

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