Page 382 - Handbook Of Integral Equations

x

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

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

5.7-3. Integrands With Nonlinearity of the Form tan[βy(t)]

x
29. y(x)+ k tan[βy(t)] dt = A.
a
This is a special case of equation 5.8.3 with f(y)= k tan(βy).
x
30. y(x)+ k tan[βy(t)] dt = Ax + B.
a
This is a special case of equation 5.8.4 with f(y)= k tan(βy).

x

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

33. y(x)+ g(t) tan[βy(t)] dt = A.
a
This is a special case of equation 5.8.7 with f(y) = tan(βy).

x tan[βy(t)]
34. y(x)+ dt = A.
0 ax + bt
This is a special case of equation 5.8.8 with f(y) = tan(βy).

x
tan[βy(t)]

35. y(x)+ √ dt = A.
2
0 ax + bt 2
This is a special case of equation 5.8.9 with f(y) = tan(βy).
x

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

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 362