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1. Volterra Integral Equations of the First Kind

1-1. Integral equations with kernels involving power-law functions

1. (x − t) y(t) dt = f(x).
2. (Ax + Bt + C) y(t) dt = f(x).
3. (x − t)n y(t) dt = f(x),n = 1, 2, ...
4. (x − t)1/2 y(t) dt = f(x).
5. (x − t)−1/2 y(t) dt = f(x). Abel equation.
6. (x − t)λ y(t) dt = f(x), 0 < λ < 1.
7. (x − t)−λ y(t) dt = f(x), 0 < λ < 1. Generalized Abel equation.

1-2. Integral equations with kernels involving exponential functions

1. _e_λ(x_−_t) y(t) dt = f(x).
2. e_λ_x+β_t_ y(t) dt = f(x).
3. [_e_λ(x_−_t) − 1] y(t) dt = f(x).
4. [_e_λ(x_−_t) + b] y(t) dt = f(x).
5. [_e_λ(x_−_t) −_e_μ(x_−_t)] y(t) dt = f(x).
6. (e_λ_x − e_λ_t)−1/2 y(t) dt = f(x).

1-3. Integral equations with kernels involving hyperbolic functions

1. cosh[λ(x − t)] y(t) dt = f(x).
2. {cosh[λ(x − t)] − 1} y(t) dt = f(x).
3. {cosh[λ(x − t)] + b} y(t) dt = f(x).
4. cosh2[λ(x − t)] y(t) dt = f(x).
5. sinh[λ(x − t)] y(t) dt = f(x).
6. {sinh[λ(x − t)] + b} y(t) dt = f(x).
7. sinh[λ(x − t)1/2] y(t) dt = f(x).

1-4. Integral equations with kernels involving logarithmic functions

1. ln(x − t) y(t) dt = f(x).
2. [ln(x − t) + A] y(t) dt = f(x).
3. (x − t)[ln(x − t) + A] y(t) dt = f(x).

1-5. Integral equations with kernels involving trigonometric functions

1. cos[λ(x − t)] y(t) dt = f(x).
2. {cos[λ(x − t)] − 1} y(t) dt = f(x).
3. {cos[λ(x − t)] + b} y(t) dt = f(x).
4. sin[λ(x − t)] y(t) dt = f(x).
5. sin[λ(x − t)1/2] y(t) dt = f(x).

1-6. Integral equations with kernels involving special functions

1. _J_0(λ(x − t)) y(t) dt = f(x).
2. _J_0(λ(x − t)1/2) y(t) dt = f(x).
3. _I_0(λ(x − t)) y(t) dt = f(x).
4. _I_0(λ(x − t)1/2) y(t) dt = f(x).

10-7. Integral equations with kernels involving arbitrary functions

1. [g(x) − g(t)] y(t) dt = f(x).
2. [g(x) − g(t) + b] y(t) dt = f(x).
3. [g(x) + h(t)] y(t) dt = f(x).
4. K(x − t) y(t) dt = f(x).
5. [g(x) − g(t)]1/2 y(t) dt = f(x).
6. [g(x) − g(t)]−1/2 y(t) dt = f(x).

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