The 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 $a(x,y)\,dy^2+2b(x,y)\,dx\,dy+c(x,y)\,dx^2=0$, 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 generic binary differential equations of this form are formally equivalent, then they are analytically equivalent.