# IE14

From Example Problems

Find the value of lambda for which the homogeneous Fredholm integral equation has a nontrivial solution, and find all the solutions.

First, divide both sides by :

The right side is a constant; therefore, the left side
must also be a constant. Thus ,
so .

Insert this in the integral equation:

Since we want a nontrivial solution, we may assume that
, so divide both sides by
; this yields

Evaluate the integral; this gives

Thus, a nontrivial solution exists only for
and the general solution in this case is
where
is an arbitrary constant.