Rigidity theorem for the equation of characteristics of a second-order linear equation of mixed type on a plane at a point where the coefficients are zero

Binary differential equations (that is, equations of the form a(x,y) dy²+2b(x,y) dx dy+c(x,y) dx²=0, where the coefficients a, b and c are analytic functions in a neighbourhood of the point $(0,0)$) are considered. A rigidity theorem is proved for degenerate singular points of such equations (that is, for $a(0,0)=b(0,0)=c(0,0)=0$): if two generic binary differential equations of this form are formally equivalent, then they are analytically equivalent. Bibliography: 36 titles.