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Separable

Definition

A separable differential equation is one where it is possible to separate variables on each side of the equation before solving it. This simplifies the process by allowing us to solve two simpler equations instead of one complex equation.

Analogy

Imagine separating your laundry into different piles based on colors before washing them. Similarly, in separable differential equations, we separate variables into different sides so that we can deal with them individually before bringing them back together.

Related terms

Differential Equation: A differential equation is an equation that relates a function with its derivatives. It involves rates of change and can be used to model various real-world phenomena.

Exact Equation: An exact differential equation is one where the total differential of a function can be expressed as a combination of its partial derivatives. Solving an exact equation involves finding a function whose derivative matches the given equation.

Homogeneous Equation: A homogeneous differential equation is one where all terms involving the dependent variable and its derivatives have the same degree. These equations can be solved by using substitution techniques to simplify them.