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b

17. y(x) – λ e µ(x–t) sin[β(x – t)]y(t) dt = f(x).
a
This is a special case of equation 4.9.18 with g 1 (x)= e µx sin(βx), h 1 (t)= e –µt cos(βt),
g 2 (x)= e µx cos(βx), and h 2 (t)= –e –µt sin(βt).

b n

18. y(x) – λ e µ(x–t) A k sin[β k (x – t)] y(t) dt = f(x), n =1, 2, ...
a
k=1
This is a special case of equation 4.9.20.
b

19. y(x) – λ te µ(x–t) sin[β(x – t)]y(t) dt = f(x).
a
This is a special case of equation 4.9.18 with g 1 (x)= e µx sin(βx), h 1 (t)= te –µt cos(βt),
g 2 (x)= e µx cos(βx), and h 2 (t)= –te –µt sin(βt).

b
20. y(x) – λ xe µ(x–t) sin[β(x – t)]y(t) dt = f(x).
a
This is a special case of equation 4.9.18 with g 1 (x)= xe µx sin(βx), h 1 (t)= e –µt cos(βt),
g 2 (x)= xe µx cos(βx), and h 2 (t)= –e –µt sin(βt).

b

21. y(x) – λ e µt tan(βx)y(t) dt = f(x).
a
µt
This is a special case of equation 4.9.1 with g(x) = tan(βx) and h(t)= e .
b

22. y(x) – λ e µx tan(βt)y(t) dt = f(x).
a
This is a special case of equation 4.9.1 with g(x)= e µx and h(t) = tan(βt).
b
23. y(x) – λ e µ(x–t) [tan(βx) – tan(βt)]y(t) dt = f(x).
a
µx
This is a special case of equation 4.9.18 with g 1 (x)= e µx tan(βx), h 1 (t)= e –µt , g 2 (x)= e ,
and h 2 (t)= –e –µt tan(βt).
b

24. y(x) – λ e µt cot(βx)y(t) dt = f(x).
a
µt
This is a special case of equation 4.9.1 with g(x) = cot(βx) and h(t)= e .

b
25. y(x) – λ e µx cot(βt)y(t) dt = f(x).
a
This is a special case of equation 4.9.1 with g(x)= e µx and h(t) = cot(βt).

4.7-4. Kernels Containing Hyperbolic and Logarithmic Functions

b
m
k
26. y(x) – λ cosh (βx)ln (µt)y(t) dt = f(x).
a
k m
This is a special case of equation 4.9.1 with g(x) = cosh (βx) and h(t)=ln (µt).

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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