An integral equation involves an unknown function under the integral sign. Most common of them is a linear integral equation
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Any linear integral equation is equivalent to a linear differential equation; e.g. the equation
to the equation
with the initial conditions
and
.
The equation (1) is of
If both limits of integration in (1) are constant, (1) is a Fredholm equation, if one limit is variable, one has a Volterra equation. In the case that
, the linear integral equation is homogeneous.
Example. Solve the Volterra equation
by using Laplace transform.
Using the convolution, the equation may be written
. Applying to this the Laplace transform, one obtains
, whence
. This corresponds the function
, which is the solution.
Solutions on some integral equations in EqWorld.
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