Page 176 - Handbook Of Integral Equations

x
tan(λt)
34. y(x) – A y(t) dt = f(x).
a tan(λx)
Solution:
x
tan(λt)
y(x)= f(x)+ A e A(x–t) f(t) dt.
tan(λx)
a
x

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

m
k
36. y(x)+ A t tan (λx)y(t) dt = f(x).
a
k
m
This is a special case of equation 2.9.2 with g(x)= –A tan (λx) and h(t)= t .
x
k
m
37. y(x)+ A x tan (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) = tan (λt).
x

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

39. y(x)+ A tan(kt)+ B + AB(x – t) tan(kt) y(t) dt = f(x).
a
This is a special case of equation 2.9.8 with λ = B and g(t)= A tan(kt).
2.5-4. Kernels Containing Cotangent
x
40. y(x) – A cot(λx)y(t) dt = f(x).
a
This is a special case of equation 2.9.2 with g(x)= A cot(λx) and h(t)=1.
Solution:
x
A/λ
y(x)= f(x)+ A cot(λx) sin(λx) f(t) dt.
a sin(λt)
x

41. y(x) – A cot(λt)y(t) dt = f(x).
a
This is a special case of equation 2.9.2 with g(x)= A and h(t) = cot(λt).
Solution:
x
A/λ
y(x)= f(x)+ A coth(λt) sin(λx) f(t) dt.
a sin(λt)
x cot(λx)
42. y(x) – A y(t) dt = f(x).
a cot(λt)
Solution:
x cot(λx)
y(x)= f(x)+ A e A(x–t) f(t) dt.
a cot(λt)

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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