Page 379 - Handbook Of Integral Equations

x

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

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

5.6-3. Other Integrands

x
10. y(x)+ g(t) ln[λy(t)] dt = A.
a
This is a special case of equation 5.8.7 with f(y) = ln(λy).
x

11. y(x)+ k sinh[λ(x – t)] ln[µy(t)] dt = Ae λx + Be –λx + C.
a
This is a special case of equation 5.8.14 with f(y)= k ln(µy).

x

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

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

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

5.7. Equations With Trigonometric Nonlinearity

5.7-1. Integrands With Nonlinearity of the Form cos[βy(t)]

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

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

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

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 359