Page 179 - Handbook Of Integral Equations

x

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

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

2.6-3. Kernels Containing Arctangent

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

14. y(x) – A arctan(λt)y(t) dt = f(x).
a
This is a special case of equation 2.9.2 with g(x)= A and h(t) = arctan(λt).

x
arctan(λx)
15. y(x) – A y(t) dt = f(x).
a arctan(λt)
Solution:
x arctan(λx)
y(x)= f(x)+ A e A(x–t) f(t) dt.
a arctan(λt)
x
arctan(λt)
16. y(x) – A y(t) dt = f(x).
a arctan(λx)
Solution:
x arctan(λt)
y(x)= f(x)+ A e A(x–t) f(t) dt.
a arctan(λx)
∞

17. y(x)+ A arctan[λ(t – x)]y(t) dt = f(x).
x
This is a special case of equation 2.9.62 with K(x)= A arctan(–λx).

x

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

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

2.6-4. Kernels Containing Arccotangent
x

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

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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