Page 384 - Handbook Of Integral Equations

x
cot[βy(t)]
48. y(x)+ dt = A.
ax + bt
0
This is a special case of equation 5.8.8 with f(y) = cot(βy).
x cot[βy(t)]
49. y(x)+ √ dt = A.
2
0 ax + bt 2
This is a special case of equation 5.8.9 with f(y) = cot(βy).
x
50. y(x)+ k e λt cot[βy(t)] dt = Be λx + C.
a
This is a special case of equation 5.8.11 with f(y)= k cot(βy).

x
51. y(x)+ k e λ(x–t) cot[βy(t)] dt = A.
a
This is a special case of equation 5.8.12 with f(y)= k cot(βy).

x

52. y(x)+ k e λ(x–t) cot[βy(t)] dt = Ae λx + B.
a
This is a special case of equation 5.8.13 with f(y)= k cot(βy).

x

53. y(x)+ k sinh[λ(x – t)] cot[βy(t)] dt = Ae λx + Be –λx + C.
a
This is a special case of equation 5.8.14 with f(y)= k cot(βy).
x

54. y(x)+ k sinh[λ(x – t)] cot[βy(t)] dt = A cosh(λx)+ B.
a
This is a special case of equation 5.8.15 with f(y)= k cot(βy).

x
55. y(x)+ k sinh[λ(x – t)] cot[βy(t)] dt = A sinh(λx)+ B.
a
This is a special case of equation 5.8.16 with f(y)= k cot(βy).
x
56. y(x)+ k sin[λ(x – t)] cot[βy(t)] dt = A sin(λx)+ B cos(λx)+ C.
a
This is a special case of equation 5.8.17 with f(y)= k cot(βy).

5.8. Equations With Nonlinearity of General Form

x

5.8-1. Equations of the Form G(···) dt = F (x)
a
x

1. K(x, t)ϕ y(t) dt = f(x).
a

The substitution w(x)= ϕ y(x) leads to the linear equation
x
K(x, t)w(t) dt = f(x).
a

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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