Page 375 - Handbook Of Integral Equations

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

22. y(x)+ k e λt sinh[βy(t)] dt = Be λx + C.
a
This is a special case of equation 5.8.11 with f(y)= k sinh(βy).
x
23. y(x)+ k e λ(x–t) sinh[βy(t)] dt = A.
a
This is a special case of equation 5.8.12 with f(y)= k sinh(βy).

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

x

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

x

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

x
28. y(x)+ k sin[λ(x – t)] sinh[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 sinh(βy).

5.5-3. Integrands With Nonlinearity of the Form tanh[βy(t)]

x

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

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

2
31. y(x)+ k (x – t) tanh[βy(t)] dt = Ax + Bx + C.
a
This is a special case of equation 5.8.5 with f(y)= k tanh(βy).

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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