Non-similar six-dimensional approximate Lie algebras on planes and invariant second order differential equations with small parametre

In this paper a problem of construction of all non-similar six-dimensional approximate Lie algebras in space of first order differential operators from two variables by known classification of approximate algebras and finding of corresponding second order invariant differential equations $y''=F_{(0)}(x,y,y')+\varepsilon F_{(1)}(x,y,y')+o(\varepsilon)$ are solved.