 Lie-symmetry determining equation for a first-order ordinary differential equation

ID: lie-symmetry-determining-equation-for-a-first-order-ordinary-differential-equation

For

u^{'} = F (x, u)

, a point-symmetry generator

V = ξ \partial_{x} + η \partial_{u}

must satisfy

η_{x} + (η_{u} - ξ_{x} - F ξ_{u}) F - ξ F_{x} - η F_{u} = 0.

u^{'} - F = 0

and restricting to its solution manifold.

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