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Exact Solutions > Integral Equations > Nonlinear Integral Equations with Variable Limit of Integration

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5. Nonlinear Integral Equations with Variable Limit of Integration

  1. y(t) y(x − t) dt = (Ax + B)eλx.
  2. y(t) y(x − t) dt = A2xμeλx.
  3. y(t) y(x − t) dt = A2 cos(λx).
  4. y(t) y(x − t) dt = A sin(λx).
  5. f(t/x) y(t) y(x − t) dt = Axμeλx.
  6. y(x) + A y2(t) dt = Bx + C.
  7. y(x) + f(t) yk(t) dt = A.
  8. y(x) + (ax + bt)−1 f(y(t)) dt = A.
  9. y(x) + f(t, y(t)) dt = g(x).
  10. y(x) + (x − t)n f(t, y(t)) dt = g(x),     n = 1, 2, ...
  11. y(x) + eλ(x−t) f(t, y(t)) dt = g(x).
  12. y(x) + sin[λ(x − t)] f(t, y(t)) dt = g(x).

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