Page 360 - Handbook Of Integral Equations

x
y(t)y(x – t)
λ
21. dt = Ax .
ax + bt
0
Solutions:
1
A λ/2 λ/2 λ/2 dz
y(x)= ± x , I = z (1 – z) .
I 0 a + bz
x
y(t)y(x – t) λx

22. dt = Ae .
0 ax + bt
Solutions:

A λx 1 b
y(x)= ± e , I = ln 1+ .
I b a
x
y(t)y(x – t)
µ λx
23. dt = Ax e .
0 ax + bt
Solutions:
1
A µ/2 λx µ/2 µ/2 dz
y(x)= ± x e , I = z (1 – z) .
I 0 a + bz
x
y(t)y(x – t)
λ
24. √ dt = Ax .
2
0 ax + bt 2
Solutions:
1
A λ/2 λ/2 λ/2 dz
y(x)= ± x , I = z (1 – z) √ .
I 0 a + bz 2
x y(t)y(x – t)
25. √ dt = Ae λx .
2
0 ax + bt 2
Solutions:
1
A λx dz
y(x)= ± e , I = √ .
I 2
0 a + bz
x
y(t)y(x – t)
µ λx
26. √ dt = Ax e .
2
0 ax + bt 2
Solutions:
1
A µ/2 λx µ/2 µ/2 dz
y(x)= ± x e , I = z (1 – z) √ .
I 0 a + bz 2
x

5.1-3. Equations of the Form G(···) dt = F (x)
0
x
λ
27. y(t)y(ax + bt) dt = Ax .
0
Solutions:
1
A λ–1 λ–1 λ–1
y(x)= ± x 2 , I = z 2 (a + bz) 2 dz.
I
0

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 340