Page 392 - Handbook Of Integral Equations

1
5. y(x)y(t) dt = A tanh(βx), Aβ >0.
0
This is a special case of equation 6.2.1 with f(x)= A tanh(βx), g(t)=1, a = 0, and b =1.

Aβ
Solutions: y(x)= ± tanh(βx).
ln cosh β

1

6. y(x)y(t) dt = A ln(βx), A(ln β – 1) > 0.
0
This is a special case of equation 6.2.1 with f(x)= A ln(βx), g(t)=1, a = 0, and b =1.

A
Solutions: y(x)= ± ln(βx).
ln β – 1

1

7. y(x)y(t) dt = A cos(βx), A >0.
0
This is a special case of equation 6.2.1 with f(x)= A cos(βx), g(t)=1, a = 0, and b =1.

Aβ
Solutions: y(x)= ± cos(βx).
sin β

1
8. y(x)y(t) dt = A sin(βx), Aβ >0.
0
This is a special case of equation 6.2.1 with f(x)= A sin(βx), g(t)=1, a = 0, and b =1.

Aβ
Solutions: y(x)= ± sin(βx).
1 – cos β

1
9. y(x)y(t) dt = A tan(βx), Aβ >0.
0
This is a special case of equation 6.2.1 with f(x)= A tan(βx), g(t)=1, a = 0, and b =1.

–Aβ
Solutions: y(x)= ± tan(βx).
ln |cos β|
1

λ
µ
10. t y(x)y(t) dt = Ax , A >0, µ + λ > –1.
0
µ
λ
This is a special case of equation 6.2.1 with f(x)= Ax , g(t)= t , a = 0, and b =1.
√ λ
Solutions: y(x)= ± A(µ + λ +1) x .
1
µt
11. e y(x)y(t) dt = Ae βx , A >0.
0
βx
µt
This is a special case of equation 6.2.1 with f(x)= Ae , g(t)= e , a = 0, and b =1.

A(µ + β) βx
Solutions: y(x)= ± µ+β e .
e – 1
© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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