Page 282 - Handbook Of Integral Equations

b A B
46. y(x) – λ + y(t) dt = f(x).
a x t
This is a special case of equation 4.9.4 with g(x)=1/x.
Solution:
A 1
y(x)= f(x)+ λ + A 2 ,
x
where A 1 and A 2 are the constants determined by the formulas presented in 4.9.4.

b

A B
47. y(x) – λ + y(t) dt = f(x).
a x + α t + β
A B
This is a special case of equation 4.9.5 with g(x)= and h(t)= .
x + α t + β
Solution:

A
y(x)= f(x)+ λ A 1 + A 2 ,
x + α
where A 1 and A 2 are the constants determined by the formulas presented in 4.9.5.

x t
b
48. y(x) – λ – y(t) dt = f(x).
a t x
This is a special case of equation 4.9.16 with g(x)= x and h(t)=1/t.
Solution:
A 2
y(x)= f(x)+ λ A 1 x + ,
x
where A 1 and A 2 are the constants determined by the formulas presented in 4.9.16.
b

Ax Bt
49. y(x) – λ + y(t) dt = f(x).
t x
a
This is a special case of equation 4.9.17 with g(x)= x and h(t)=1/t.
Solution:

A 2
y(x)= f(x)+ λ A 1 x + ,
x
where A 1 and A 2 are the constants determined by the formulas presented in 4.9.17.

b x + α t + α
50. y(x) – λ A + B y(t) dt = f(x).
a t + β x + β
1
This is a special case of equation 4.9.17 with g(x)= x + α and h(t)= .
t + β
Solution:
A 2
y(x)= f(x)+ λ A 1 (x + α)+ ,
x + β
where A 1 and A 2 are the constants determined by the formulas presented in 4.9.17.
b
(x + α) n (t + α) n
51. y(x) – λ A + B y(t) dt = f(x), n, m = 0,1,2, ...
(t + β) m (x + β) m
a
n
This is a special case of equation 4.9.17 with g(x)=(x + α) and h(t)=(t + β) –m .
Solution:

n
y(x)= f(x)+ λ A 1 (x + α) + A 2 ,
(x + β) m
where A 1 and A 2 are the constants determined by the formulas presented in 4.9.17.

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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