# Difference between revisions of "Exact differential equation"

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Suppose you are given an equation of the form: | Suppose you are given an equation of the form: | ||

− | :<math>M(t,y) + N(t,y)y' = 0\,</math> or <math>M(t,y) dt + N(t,y) dy = 0\,</math> (equation 1) | + | :<math>M(t,y) + N(t,y)y' = 0\,</math> or <math>M(t,y) dt + N(t,y) dy = 0\,</math> (we will call this equation 1) |

## Revision as of 12:55, 2 August 2010

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 (we will call this equation 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.