Page 178 - Handbook Of Integral Equations

x

2. y(x) – A arccos(λt)y(t) dt = f(x).
a
This is a special case of equation 2.9.2 with g(x)= A and h(t) = arccos(λt).

x
arccos(λx)
3. y(x) – A y(t) dt = f(x).
a arccos(λt)
Solution:
x
arccos(λx)
y(x)= f(x)+ A e A(x–t) f(t) dt.
arccos(λt)
a
x
arccos(λt)
4. y(x) – A y(t) dt = f(x).
a arccos(λx)
Solution:
x
arccos(λt)
y(x)= f(x)+ A e A(x–t) f(t) dt.
a arccos(λx)
x

5. y(x) – A arccos(kx)+ B – AB(x – t) arccos(kx) y(t) dt = f(x).
a
This is a special case of equation 2.9.7 with λ = B and g(x)= A arccos(kx).
x

6. y(x)+ A arccos(kt)+ B + AB(x – t) arccos(kt) y(t) dt = f(x).
a
This is a special case of equation 2.9.8 with λ = B and g(t)= A arccos(kt).

2.6-2. Kernels Containing Arcsine

x

7. y(x) – A arcsin(λx)y(t) dt = f(x).
a
This is a special case of equation 2.9.2 with g(x)= A arcsin(λx) and h(t)=1.
x

8. y(x) – A arcsin(λt)y(t) dt = f(x).
a
This is a special case of equation 2.9.2 with g(x)= A and h(t) = arcsin(λt).

x
arcsin(λx)
9. y(x) – A y(t) dt = f(x).
a arcsin(λt)
Solution:
x
arcsin(λx)
y(x)= f(x)+ A e A(x–t) f(t) dt.
a arcsin(λt)
x
arcsin(λt)
10. y(x) – A y(t) dt = f(x).
a arcsin(λx)
Solution:
x arcsin(λt)
y(x)= f(x)+ A e A(x–t) f(t) dt.
a arcsin(λx)

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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