Page 190 - Handbook Of Integral Equations

x

11. y(x) – A Y 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)= Y ν (λt).
x Y ν (λx)
12. y(x) – A y(t) dt = f(x).
a Y ν (λt)
Solution:
x
Y ν (λx)
y(x)= f(x)+ A e A(x–t) f(t) dt.
a Y ν (λt)
x Y ν (λt)
13. y(x) – A y(t) dt = f(x).
a Y ν (λx)
Solution:
x
Y ν (λt)
y(x)= f(x)+ A e A(x–t) f(t) dt.
a Y ν (λx)
∞

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

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

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

2.8-2. Kernels Containing Modified Bessel Functions

x
17. y(x)– A I ν (λx)y(t) dt = f(x).
a
This is a special case of equation 2.9.2 with g(x)= AI ν (λx) and h(t)=1.
x
18. y(x)– A I 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)= I ν (λt).
x
I ν (λx)
19. y(x)– A y(t) dt = f(x).
I ν (λt)
a
Solution:
x A(x–t) ν (λx)
I
y(x)= f(x)+ A e f(t) dt.
a I ν (λt)
x
I ν (λt)
20. y(x)– A y(t) dt = f(x).
a I ν (λx)
Solution:
x I ν (λt)
y(x)= f(x)+ A e A(x–t) f(t) dt.
a I ν (λx)

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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