exact differential equation
is called an exact differential equation, if the condition
is true in .
By (2), the left hand side of (1) is the total differential of a function, there is a function such that the equation (1) reads
whence its general integral is
The solution function can be calculated as the line integral
along any curve connecting an arbitrarily chosen point and the point in the region (the integrating factor is now ).
Example. Solve the differential equation
This equation is exact, since
If we use as the integrating way the broken line from to and from this to , the integral (3) is simply
Thus we have the general integral
of the given differential equation.
|Title||exact differential equation|
|Date of creation||2013-03-22 18:06:17|
|Last modified on||2013-03-22 18:06:17|
|Last modified by||pahio (2872)|
|Defines||exact differential equation|