Let
be a region in
and let the functions
,
have continuous partial derivatives in
. The first order differential equation
or
![]() |
(1) |
is true in
Then there is a function
such that the equation (1) has the form
whence its general integral is
The solution function
can be calculated as the line integral
![]() |
(2) |
Example. Solve the differential equation
This equation is exact, since
If we use as the integrating way the broken line from
Thus we have the general integral
of the given differential equation.
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