An **exact differential equation** is an ordinary differential equation in the form

If this is the case, we can assume and are the partial derivatives of an unknown function , due to the symmetry of second order partial derivatives. The function can now be written as

Since only constants have derivatives of 0, . Now can be integrated in terms of to find . Since this is a partial derivative in terms of , any functions of will be lost, so instead of adding a constant of integration, we will add . can be found by integrating in terms of , yielding the final solution is:

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