Group classification of ODE y‴=F(x,y,y′)y‴=F(x,y,y′)

• Group classification of third-order ODEs, not involving the second derivative, is carried out.
• Lie algebra of the equivalence group for the equations in question is computed.
• The results are compared with Lie’s similar results for second-order equations.

In his extensive work of 1884 on the group classification of ordinary differential equations Lie performed, inter alia, the group classification of the particular type of the second-order equations y″=F(x,y)y″=F(x,y). In the present paper we extend Lie’s classification to the third-order equations y‴=F(x,y,y′)y‴=F(x,y,y′).