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    First order ordinary differential equation

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    In order to solve differential equations, it is helpful to classify them as belonging to one or more categories. In this entry we will consider three common classes of first order
    ordinary differential equations (ODEs): separable, exact and linear.
    We will show how each class is defined.

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    Separable
    Consider an ODE of the form
    dx/dt= f(x, t), (1)
    where f(x, t) is some function of x and t. Equation 1 is called separable if we can write the function
    f(x, t) as follows:
    f(x, t) = h(t)/g(x) ,
    where h(t) and ...

    Solution Summary

    This shows how to define three common classes of first order ordinary differential equations (ODEs): separable, exact and linear.

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