Page 177 - Handbook Of Integral Equations

x
cot(λt)
43. y(x) – A y(t) dt = f(x).
a cot(λx)
Solution:
x
cot(λt)
y(x)= f(x)+ A e A(x–t) f(t) dt.
a cot(λx)
x
k
m
44. y(x)+ A t cot (λx)y(t) dt = f(x).
a
k
m
This is a special case of equation 2.9.2 with g(x)= –A cot (λx) and h(t)= t .
x

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

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

47. y(x)+ A cot(kt)+ B + AB(x – t) cot(kt) y(t) dt = f(x).
a
This is a special case of equation 2.9.8 with λ = B and g(t)= A cot(kt).
2.5-5. Kernels Containing Combinations of Trigonometric Functions
x

k
m
48. y(x) – A cos (λx) sin (µt)y(t) dt = f(x).
a
m
k
This is a special case of equation 2.9.2 with g(x)= A cos (λx) and h(t) = sin (µt).
x

49. y(x) – A + B cos(λx) – B(x – t)[λ sin(λx)+ A cos(λx)] y(t) dt = f(x).
a
This is a special case of equation 2.9.38 with b = B and g(x)= A.
x

50. y(x) – A + B sin(λx)+ B(x – t)[λ cos(λx) – A sin(λx)] y(t) dt = f(x).
a
This is a special case of equation 2.9.39 with b = B and g(x)= A.
x

m
k
51. y(x) – A tan (λx) cot (µt)y(t) dt = f(x).
a
m
k
This is a special case of equation 2.9.2 with g(x)= A tan (λx) and h(t) = cot (µt).
2.6. Equations Whose Kernels Contain Inverse
Trigonometric Functions
2.6-1. Kernels Containing Arccosine

x
1. y(x) – A arccos(λx)y(t) dt = f(x).
a
This is a special case of equation 2.9.2 with g(x)= A arccos(λx) and h(t)=1.

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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