Difference between revisions of "Exact differential equation"

From Conservapedia
Jump to: navigation, search
Line 3: Line 3:
 
Suppose you are given an equation of the form:
 
Suppose you are given an equation of the form:
  
(1):<math>M(t,y) + N(t,y)y' = 0\,</math>  or  <math>M(t,y) dt + N(t,y) dy = 0\,</math>
+
:(1)     <math>M(t,y) + N(t,y)y' = 0\,</math>  or  <math>M(t,y) dt + N(t,y) dy = 0\,</math>
  
 
Before we begin solving it, we must first check that the equation is exact. This means that:
 
Before we begin solving it, we must first check that the equation is exact. This means that:

Revision as of 13:54, 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:

(1) or

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.