Solution of an Integrodifferential Equation Containing Linear Functions of a Special Form in the Coefficients

An integrodifferential equation of arbitrary order is solved explicitly. Integrals in the equation are understood in the sense of the finite part according to Hadamard. The equation is given on a closed curve located on the complex plane. The coefficients of the equation are variables and have a special form. The generalized formulas of Sokhotsky, the theory of the Riemann boundary-value problem, and the method of variation of arbitrary constants are used for the solution. An example is given.