The differential equation

is an exact equation if

**Steps in Solving an Exact Equation**

- Let .
- Write the equation in Step 1 into the form

and integrate it partially in terms of x holding y as constant.

- Differentiate partially in terms of y the result in Step 2 holding x as constant.
- Equate the result in Step 3 to N and collect similar terms.
- Integrate the result in Step 4 with respect to y, holding x as constant.
- Substitute the result in Step 5 to the result in Step 2 and equate the result to a constant c.

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