Page 293 - Handbook Of Integral Equations

b

18. y(x) – λ (x – t)e γx y(t) dt = f(x).
a
γx
This is a special case of equation 4.9.10 with A =0, B = 1, and h(x)= e .

b
19. y(x) – λ (x – t)e γx+µt y(t) dt = f(x).
a
µt
γx
γx
This is a special case of equation 4.9.18 with g 1 (x)= xe , h 1 (t)= e , g 2 (x)= e , and
µt
h 2 (t)= –te .
b
20. y(x) – λ [A +(Bx + Ct)e γx ]y(t) dt = f(x).
a
γx
This is a special case of equation 4.9.11 with h(x)= e .
b
2
2
21. y(x) – λ (x + t )e γ(x+t) y(t) dt = f(x).
0
2 γx
γt
This is a special case of equation 4.9.15 with g(x)= x e and h(t)= e .

b
2
2
22. y(x) – λ (x – t )e γ(x–t) y(t) dt = f(x).
0
2 γx
γx
This is a special case of equation 4.9.18 with g 1 (x)= x e , h 1 (t)= e –γt , g 2 (x)= e , and
2 –γt
h 2 (t)= –t e .
b

n
n
23. y(x) – λ (Ax + Bt )e αx+βt y(t) dt = f(x), n =1, 2, ...
0
n αx
βt
This is a special case of equation 4.9.18 with g 1 (x)= x e , h 1 (t)= Ae , g 2 (x)= e αx , and
n βt
h 2 (t)= Bt e .
n
b
ν k α k x+β k t
24. y(x) – λ A k t e y(t) dt = f(x), n =1, 2, ...
a
k=1
ν k β k t
This is a special case of equation 4.9.20 with g k (x)= e α k x and h k (t)= A k t e .
n
b
ν k α k x+β k t
25. y(x) – λ A k x e y(t) dt = f(x), n =1, 2, ...
a
k=1
ν k α k x
This is a special case of equation 4.9.20 with g k (x)= A k x e and h k (t)= e β k t .
b
n γ(x–t)
26. y(x) – λ (x – t) e y(t) dt = f(x), n =1, 2, ...
a
This is a special case of equation 4.9.20.
b

n αx+βt
27. y(x) – λ (x – t) e y(t) dt = f(x), n =1, 2, ...
a
This is a special case of equation 4.9.20.

b
n αx+βt
28. y(x) – λ (Ax + Bt) e y(t) dt = f(x), n =1, 2, ...
a
This is a special case of equation 4.9.20.
© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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