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First order ordinary differential equation

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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