ON ONE OVER DETERMINED SYSTEM OF FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONS WITH ONE SINGULAR LINE
In this paper, we study a redefined system of first-order partial differential equations with a single singular line with two unknown functions. When the compatibility conditions are met, the solution manifolds are found explicitly, in terms of one arbitrary constant y and one arbitrary function. Using the found solution, problems with initial data( Cauchy-type problems) are set and solved.