A separable differential equation is an ordinary differential equation that can be separated into two integrals; that is, in the form


They are arguably the simplest ODEs to solve, as they will always have the solution

\int\dfrac{dy}{g(y)}=\int f(x)dx

If f(x) is equal to some constant, the DE is an autonomous differential equation. For example:

\int\dfrac{dy}{y}=\int x^2dx
y=\pm C_4e^{\frac{x^3}{3}}

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