Page 377 - Handbook Of Integral Equations

5.5-4. Integrands With Nonlinearity of the Form coth[βy(t)]

x

43. y(x)+ k coth[βy(t)] dt = A.
a
This is a special case of equation 5.8.3 with f(y)= k coth(βy).

x

44. y(x)+ k coth[βy(t)] dt = Ax + B.
a
This is a special case of equation 5.8.4 with f(y)= k coth(βy).

x

2
45. y(x)+ k (x – t) coth[βy(t)] dt = Ax + Bx + C.
a
This is a special case of equation 5.8.5 with f(y)= k coth(βy).
x
λ
46. y(x)+ k t coth[βy(t)] dt = Bx λ+1 + C.
a
This is a special case of equation 5.8.6 with f(y)= k coth(βy).

x
47. y(x)+ g(t) coth[βy(t)] dt = A.
a
This is a special case of equation 5.8.7 with f(y) = coth(βy).
x
coth[βy(t)]
48. y(x)+ dt = A.
0 ax + bt
This is a special case of equation 5.8.8 with f(y) = coth(βy).

x coth[βy(t)]
49. y(x)+ √ dt = A.
2
0 ax + bt 2
This is a special case of equation 5.8.9 with f(y) = coth(βy).

x

50. y(x)+ k e λt coth[βy(t)] dt = Be λx + C.
a
This is a special case of equation 5.8.11 with f(y)= k coth(βy).

x

51. y(x)+ k e λ(x–t) coth[βy(t)] dt = A.
a
This is a special case of equation 5.8.12 with f(y)= k coth(βy).

x
52. y(x)+ k e λ(x–t) coth[βy(t)] dt = Ae λx + B.
a
This is a special case of equation 5.8.13 with f(y)= k coth(βy).
x
53. y(x)+ k sinh[λ(x – t)] coth[βy(t)] dt = Ae λx + Be –λx + C.
a
This is a special case of equation 5.8.14 with f(y)= k coth(βy).

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 357