Page 444 - Handbook Of Integral Equations

b

70. y(x)+ y(ξ)f t, y(t) dt = g(x), ξ = x + ϕ(t).
a
1 .For g(x)= n A k exp(λ k x) the equation has a solution of the form
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k=1
n

y(x)= B k exp(λ k x),
k=1

where the constants B k are determined from the nonlinear algebraic (or transcendental) system

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B k + B k F k (B) – A k =0, k =1, ... , n,
n
b
%
%

B = {B 1 , ... , B n }, F k (B)= f t, B m exp(λ m t) exp λ k ϕ(t) dt.
a
m=1
2 . Solutions for some other functions g(x) can be found in items 2 –11 of equation 6.8.66.
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© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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