# Difference between revisions of "Exact differential equation"

An exact differential equation is a differential equation that can be solved in the following manner.

Suppose you are given an equation of the form:

 or  (1)

Before we begin solving it, we must first check that the equation is exact. This means that:



To find the solution of this equation, we assume that the solution is φ = constant. We assume that  and . (If we substitute M and N back into (1), it yields , which makes sense.)

To find , manipulate the substitutions of M and N to get  and . Integrate both sides. To get the main function φ write the sum of each term found in each equation. For terms that appear in both equations, only write them once.

To solve the expression for , use the quadratic formula.