Page 191 - Handbook Of Integral Equations

∞

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

x

22. y(x) – AI ν (kx)+ B – AB(x – t)I ν (kx) y(t) dt = f(x).
a
This is a special case of equation 2.9.7 with λ = B and g(x)= AI ν (kx).

x

23. y(x)+ AI ν (kt)+ B + AB(x – t)I ν (kt) y(t) dt = f(x).
a
This is a special case of equation 2.9.8 with λ = B and g(t)= AI ν (kt).

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

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

x K ν (λx)
26. y(x) – A y(t) dt = f(x).
a K ν (λt)
Solution:
x K ν (λx)
y(x)= f(x)+ A e A(x–t) f(t) dt.
a K ν (λt)
x
K ν (λt)
27. y(x) – A y(t) dt = f(x).
a K ν (λx)
Solution:
x
K ν (λt)
y(x)= f(x)+ A e A(x–t) f(t) dt.
a K ν (λx)
∞

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

x

29. y(x) – AK ν (kx)+ B – AB(x – t)K ν (kx) y(t) dt = f(x).
a
This is a special case of equation 2.9.7 with λ = B and g(x)= AK ν (kx).
x

30. y(x)+ AK ν (kt)+ B + AB(x – t)K ν (kt) y(t) dt = f(x).
a
This is a special case of equation 2.9.8 with λ = B and g(t)= AK ν (kt).

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 170