Page 285 - Handbook Of Integral Equations

b
µ
60. y(x) – λ (A + Bxt + Ct µ+1 )y(t) dt = f(x).
a
µ
This is a special case of equation 4.9.9 with h(t)= t .
Solution:
y(x)= f(x)+ λ(A 1 + A 2 x),

where A 1 and A 2 are the constants determined by the formulas presented in 4.9.9.

b
β µ
α
61. y(x) – λ (At + Bx t + Ct µ+γ )y(t) dt = f(x).
a
α
β
This is a special case of equation 4.9.18 with g 1 (x)=1, h 1 (t)= At + Ct µ+γ , g 2 (x)= x , and
µ
h 2 (t)= Bt .
Solution:
β
y(x)= f(x)+ λ(A 1 + A 2 x ),
where A 1 and A 2 are the constants determined by the formulas presented in 4.9.18.

b
β γ
µ ν
α γ
62. y(x) – λ (Ax t + Bx t + Cx t )y(t) dt = f(x).
a
γ
β
µ
α
This is a special case of equation 4.9.18 with g 1 (x)= Ax + Bx , h 1 (t)= t , g 2 (x)= x , and
ν
h 2 (t)= Ct .
Solution:
µ
α
β
y(x)= f(x)+ λ[A 1 (Ax + Bx )+ A 2 x ],
where A 1 and A 2 are the constants determined by the formulas presented in 4.9.18.
(x + p 1 ) β (x + p 2 ) µ
b
63. y(x) – λ A + B y(t) dt = f(x).
a (t + q 1 ) γ (t + q 2 ) δ
–γ
β
This is a special case of equation 4.9.18 with g 1 (x)=(x + p 1 ) , h 1 (t)= A(t + q 1 ) , g 2 (x)=
µ
–δ
(x + p 2 ) , and h 2 (t)= B(t + q 2 ) .
Solution:

β µ
y(x)= f(x)+ λ A 1 (x + p 1 ) + A 2 (x + p 2 ) ,
where A 1 and A 2 are the constants determined by the formulas presented in 4.9.18.
γ
µ
b

x + a x + c
64. y(x) – λ A ν + B δ y(t) dt = f(x).
a t + b t + d
A γ
µ
This is a special case of equation 4.9.18 with g 1 (x)= x + a, h 1 (t)= , g 2 (x)= x + c,
t + b
ν
B
and h 2 (t)= .
δ
t + d
Solution:
µ
γ
y(x)= f(x)+ λ[A 1 (x + a)+ A 2 (x + c)],
where A 1 and A 2 are the constants determined by the formulas presented in 4.9.18.
© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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