Page 381 - Handbook Of Integral Equations

5.7-2. Integrands With Nonlinearity of the Form sin[βy(t)]

x

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

x

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

x

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

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

x sin[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) = sin(βy).

x

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

x

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

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

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 361