Page 217 - Handbook Of Integral Equations

Then the solution of the more complicated integral equation

x
g(x)
y(x)+ K(x, t) y(t) dt = f(x) (3)
a g(t)
has the form
x
g(x)
y(x)= f(x)+ R(x, t) f(t) dt. (4)
a g(t)
Below are formulas for the solutions of integral equations of the form (3) for some specific func-
tions g(x). In all cases, it is assumed that the solution of equation (1) is known and is given
by (2).

◦
1 . The solution of the equation
x
λ
y(x)+ K(x, t)(x/t) y(t) dt = f(x)
a
has the form
x
λ
y(x)= f(x)+ R(x, t)(x/t) f(t) dt.
a
2 . The solution of the equation
◦
x
y(x)+ K(x, t)e λ(x–t) y(t) dt = f(x)
a
has the form
x
y(x)= f(x)+ R(x, t)e λ(x–t) f(t) dt.
a

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 196