Page 97 - Handbook Of Integral Equations

x

µ(x–t) ν
76. Ae + B tan (λx) y(t) dt = f(x).
a
ν
µx
This is a special case of equation 1.9.15 with g 1 (x)= Ae , h 1 (t)= e –µt , g 2 (x)= B tan (λx),
and h 2 (t)=1.
x

µ(x–t) ν
77. Ae + B tan (λt) y(t) dt = f(x).
a
µx
This is a special case of equation 1.9.15 with g 1 (x)= Ae , h 1 (t)= e –µt , g 2 (x)= B, and
ν
h 2 (t) = tan (λt).
x

λ
λ

78. e µ(x–t) A cot x + B cot t y(t) dt = f(x).
a
The substitution w(x)= e –µx y(x) leads to an equation of the form 1.5.90:
x
λ λ
–µx
A cot x + B cot t w(t) dt = e f(x).
a
x

β
λ

79. e µ(x–t) A cot x + B cot t + C y(t) dt = f(x).
a
The substitution w(x)= e –µx y(x) leads to an equation of the form 1.9.6:
x
λ β
–µx
A cot x + B cot t + C w(t) dt = e f(x).
a
x

µ(x–t) ν
80. Ae + B cot (λx) y(t) dt = f(x).
a
µx
ν
This is a special case of equation 1.9.15 with g 1 (x)= Ae , h 1 (t)= e –µt , g 2 (x)= B cot (λx),
and h 2 (t)=1.
x

µ(x–t) ν
81. Ae + B cot (λt) y(t) dt = f(x).
a
µx
This is a special case of equation 1.9.15 with g 1 (x)= Ae , h 1 (t)= e –µt , g 2 (x)= B, and
ν
h 2 (t) = cot (λt).
1.7-4. Kernels Containing Hyperbolic and Logarithmic Functions
x
β γ
82. A cosh (λx)+ B ln (µt)+ C y(t) dt = f(x).
a
β γ
This is a special case of equation 1.9.6 with g(x)= A cosh (λx) and h(t)= B ln (µt)+ C.
x

β γ
83. A cosh (λt)+ B ln (µx)+ C y(t) dt = f(x).
a
γ
β
This is a special case of equation 1.9.6 with g(x)= B ln (µx)+ C and h(t)= A cosh (λt).
x
β γ
84. A sinh (λx)+ B ln (µt)+ C y(t) dt = f(x).
a
β γ
This is a special case of equation 1.9.6 with g(x)= A sinh (λx) and h(t)= B ln (µt)+ C.
© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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