Page 304 - Handbook Of Integral Equations

∞
6. y(x) – λ cos(xt)y(t) dt = f(x).
0
Solution:
∞
f(x) λ
y(x)= π + π cos(xt)f(t) dt,
1 – λ 2 1 – λ 2
2 2 0

where λ ≠ ± 2/π.
•
Reference: M. L. Krasnov, A. I. Kisilev, and G. I. Makarenko (1971).
n
b

7. y(x) – λ A k cos[β k (x – t)] y(t) dt = f(x), n =1, 2, ...
a
k=1
This equation can be reduced to a special case of equation 4.9.20; the formula cos[β(x – t)] =
cos(βx) cos(βt) + sin(βx) sin(βt) must be used.

b cos(βx)
8. y(x) – λ y(t) dt = f(x).
a cos(βt)
1
This is a special case of equation 4.9.1 with g(x) = cos(βx) and h(t)= .
cos(βt)
b cos(βt)

9. y(x) – λ y(t) dt = f(x).
a cos(βx)
1
This is a special case of equation 4.9.1 with g(x)= and h(t) = cos(βt).
cos(βx)
b

m
k
10. y(x) – λ cos (βx) cos (µt)y(t) dt = f(x).
a
m
k
This is a special case of equation 4.9.1 with g(x) = cos (βx) and h(t) = cos (µt).
b
k
m
11. y(x) – λ t cos (βx)y(t) dt = f(x).
a
k
m
This is a special case of equation 4.9.1 with g(x) = cos (βx) and h(t)= t .
b
m
k
12. y(x) – λ x cos (βt)y(t) dt = f(x).
a
m
k
This is a special case of equation 4.9.1 with g(x)= x and h(t) = cos (βt).
b

13. y(x) – λ [A + B(x – t) cos(βx)]y(t) dt = f(x).
a
This is a special case of equation 4.9.10 with h(x) = cos(βx).
b
14. y(x) – λ [A + B(x – t) cos(βt)]y(t) dt = f(x).
a
This is a special case of equation 4.9.8 with h(t) = cos(βt).

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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