On a class of differential equations in mechanics of continua

connecting the real and the imaginary parts of an analytic function of x-\-iy. This similarity suggests an integration theory similar in pattern to that of the complex function theory. The fundamentals of such theory are presented in this paper. (A more elaborate mathematical treatment, containing all proofs, will be published elsewhere). The theory will be illustrated by some physical examples. In treating these examples our aim is not to obtain new results in mechanics but rather to present known facts from a simpler and more unified point of view. In what follows we suppose that the coefficients n (i = 1, 2) are positive analytic functions of the real variable y. Then the equations (1.2) are of