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based on an earlier version of the Wolfram Language.
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Exact Equations

Here is an example of an exact ODE.
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This verifies the solution.
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Here is a contour plot of the solution.
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If an equation is not exact, it may be possible to find an integrating factor (a multiplier for the functions P and Q, defined previously) that converts the equation into exact form. DSolve tries a variety of techniques to automatically find integrating factors in such situations.