Exact differential equation
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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.
