Page 374 - Handbook Of Integral Equations

x

10. y(x)+ k e λ(x–t) cosh[βy(t)] dt = Ae λx + B.
a
This is a special case of equation 5.8.13 with f(y)= k cosh(βy).

x
11. y(x)+ k sinh[λ(x – t)] cosh[βy(t)] dt = Ae λx + Be –λx + C.
a
This is a special case of equation 5.8.14 with f(y)= k cosh(βy).
x
12. y(x)+ k sinh[λ(x – t)] cosh[βy(t)] dt = A cosh(λx)+ B.
a
This is a special case of equation 5.8.15 with f(y)= k cosh(βy).

x

13. y(x)+ k sinh[λ(x – t)] cosh[βy(t)] dt = A sinh(λx)+ B.
a
This is a special case of equation 5.8.16 with f(y)= k cosh(βy).

x
14. y(x)+ k sin[λ(x – t)] cosh[βy(t)] dt = A sin(λx)+ B cos(λx)+ C.
a
This is a special case of equation 5.8.17 with f(y)= k cosh(βy).

5.5-2. Integrands With Nonlinearity of the Form sinh[βy(t)]

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

x

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

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

x

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

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 354