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Definition: Suppose dy/dx = f(x,y) can be written in the form M(x) + N(y)(dy/dx) = 0. Such an equation is said to be separable, because if it is written in the differential form M(x)dx + N(y)dy = 0, then, if you wish, terms involving each variable may be placed on opposite sides of the equation.
Source: Elementary Differential Equations and Boundary Value Problems - William Boyce & Richard DiPrima