Page 419 - Handbook Of Integral Equations

6.7. Equations With Trigonometric Nonlinearity

6.7-1. Integrands With Nonlinearity of the Form cos[βy(t)]

b

1. y(x)+ A cos[βy(t)] dt = g(x).
a
This is a special case of equation 6.8.27 with f(t, y)= A cos(βy).

b

µ
k
2. y(x)+ A t cos [βy(t)] dt = g(x).
a
µ
k
This is a special case of equation 6.8.27 with f(t, y)= At cos (βy).
b

3. y(x)+ A cos(µt) cos[βy(t)] dt = g(x).
a
This is a special case of equation 6.8.27 with f(t, y)= A cos(µt) cos(βy).
b
4. y(x)+ A e λ(x–t) cos[βy(t)] dt = g(x).
a
This is a special case of equation 6.8.28 with f(t, y)= A cos(βy).
b

5. y(x)+ g(x) cos[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.29 with f(t, y) = cos(βy).

b
6. y(x)+ A cosh(λx + µt) cos[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.31 with f(t, y)= A cos(βy).

b

7. y(x)+ A sinh(λx + µt) cos[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.32 with f(t, y)= A cos(βy).
b

8. y(x)+ A cos(λx + µt) cos[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.33 with f(t, y)= A cos(βy).

b
9. y(x)+ A sin(λx + µt) cos[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.34 with f(t, y)= A cos(βy).

6.7-2. Integrands With Nonlinearity of the Form sin[βy(t)]

b
10. y(x)+ A sin[βy(t)] dt = g(x).
a
This is a special case of equation 6.8.27 with f(t, y)= A sin(βy).

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 399