Page 378 - Handbook Of Integral Equations

x

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

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

x

56. y(x)+ k sin[λ(x – t)] coth[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 coth(βy).

5.6. Equations With Logarithmic Nonlinearity

5.6-1. Integrands Containing Power-Law Functions of x and t

x

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

x

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

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

λ
4. y(x)+ k t ln[µy(t)] dt = Bx λ+1 + C.
a
This is a special case of equation 5.8.6 with f(y)= k ln(µy).
x
ln[λy(t)]

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

6. y(x)+ √ dt = A.
2
0 ax + bt 2
This is a special case of equation 5.8.9 with f(y) = ln(λy).
5.6-2. Integrands Containing Exponential Functions of x and t

x

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

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 358