Page 164 - Handbook Of Integral Equations

x

43. y(x) – A coth(λt)y(t) dt = f(x).
a
This is a special case of equation 2.9.2 with g(x)= A and h(t) = coth(λt).
Solution:
x sinh(λx)
A/λ
y(x)= f(x)+ A coth(λt) f(t) dt.
a sinh(λt)
x
coth(λt)
44. y(x) – A y(t) dt = f(x).
a coth(λx)
Solution:
x
coth(λt)
y(x)= f(x)+ A e A(x–t) f(t) dt.
coth(λx)
a
x coth(λx)
45. y(x) – A y(t) dt = f(x).
a coth(λt)
Solution:
x coth(λx)
y(x)= f(x)+ A e A(x–t) f(t) dt.
a coth(λt)
x
k
m
46. y(x) – A coth (λx) coth (µt)y(t) dt = f(x).
a
m
k
This is a special case of equation 2.9.2 with g(x)= A coth (λx) and h(t) = coth (µt).
x
m
k
47. y(x)+ A t coth (λx)y(t) dt = f(x).
a
k
m
This is a special case of equation 2.9.2 with g(x)= –A coth (λx) and h(t)= t .
x

m
k
48. y(x)+ A x coth (λt)y(t) dt = f(x).
a
m
k
This is a special case of equation 2.9.2 with g(x)= –Ax and h(t) = coth (λt).
∞

49. y(x)+ A coth[λ(t – x)]y(t) dt = f(x).
x
This is a special case of equation 2.9.62 with K(z)= A coth(–λz).
∞

√
50. y(x)+ A coth λ t – x y(t) dt = f(x).
x
√
This is a special case of equation 2.9.62 with K(z)= A coth λ –z .
x

51. y(x) – A coth(kx)+ B – AB(x – t) coth(kx) y(t) dt = f(x).
a
This is a special case of equation 2.9.7 with λ = B and g(x)= A coth(kx).
x

52. y(x)+ A coth(kt)+ B + AB(x – t) coth(kt) y(t) dt = f(x).
a
This is a special case of equation 2.9.8 with λ = B and g(t)= A coth(kt).

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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