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15.1 Definition

A first order differential equation is an equation of the form


If F(x, y) is a function of x only, that is if F(x, y) = f(x), the differential equation becomes

and can be integrated


To specify y, we need to know the value  of y(x1) (initial condition) or some equivalent piece of information.

Examples with dy / dx = F(x)

Example 1

Example 2