On a class of Differential Equations whose solutions satisfy Integral Equations

The science of the solution of Differential Equations has been in great measure systematized by the aid of ideas borrowed from the Theory of Functions, the equations being classified according to the singularities possessed by their solutions. In the case of linear Differential Equations of the second order the solutions can have no singularities except at the singularities of the functions q(x) and r(x) (and possibly also at x = ∞ ): these equations may therefore be classified simply according to the number and nature of these singularities.