Page 396 - Handbook Of Integral Equations

b
βt 2
28. y(x)+ A e y (t) dt = Be µx .
a
µx
This is a special case of equation 6.2.22 with g(t)= Ae βt and f(x)= Be .
b
2
β
µ
29. y(x)+ A x y (t) dt = Bx .
a
β
µ
This is a special case of equation 6.2.23 with g(x)= Ax and f(x)= Bx .
b

30. y(x)+ A e βx 2 µx .
y (t) dt = Be
a
µx
This is a special case of equation 6.2.23 with g(x)= Ae βx and f(x)= Be .
b

6.1-4. Equations of the Form y(x)+ K(x, t)y(x)y(t) dt = F (x)
a
b

β
µ
31. y(x)+ A t y(x)y(t) dt = Bx .
a
µ
β
This is a special case of equation 6.2.25 with g(t)= At and f(x)= Bx .
b

βt
32. y(x)+ A e y(x)y(t) dt = Be µx .
a
µx
This is a special case of equation 6.2.25 with g(t)= Ae βt and f(x)= Be .
b

µ
β
33. y(x)+ A x y(x)y(t) dt = Bx .
a
β
µ
This is a special case of equation 6.2.26 with g(x)= Ax and f(x)= Bx .
b

34. y(x)+ A e βx y(x)y(t) dt = Be µx .
a
µx
This is a special case of equation 6.2.26 with g(x)= Ae βx and f(x)= Be .
b

6.1-5. Equations of the Form y(x)+ G(···) dt = F (x)
a
1

35. y(x)+ A y(t)y(xt) dt =0.
0
This is a special case of equation 6.2.30 with f(t)= A, a = 0, and b =1.
◦
1 . Solutions:
1 C (I 1 – I 0 )x + I 1 – I 2 C
y 1 (x)= – (2C +1)x , y 2 (x)= x ,
A I 0 I 2 – I 2
1
A
I m = , m =0, 1, 2,
2C + m +1
where C is an arbitrary nonnegative constant.
k
There are more complicated solutions of the form y(x)= x C n B k x , where C is an
k=0
arbitrary constant and the coefficients B k can be found from the corresponding system of
algebraic equations.
© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 376