Abstract
The main purpose of the present paper consists an investigation of an elliptic system in the plane with Laplace operator in differential part. Within the scope of this target, investigation of the continuous solutions of a class of complex partial second order differential equations in the plane in explicit form are constructed. Robin boundary value problem for second order elliptic system in the plane with singular coefficients in unbounded angular domain is solved.In this article, a new method for construction of the general solution of second order ordinary differential equation with variable coefficients developed by A. Tungatarov is used.