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Ordinary differential equation

Lie point symmetry of an ordinary differential equation

Prolongation of a vector field

{title2=$\operatorname{pr}^{(1)}V$}

For $V=\xi(x,u)\partial_x+\eta(x,u)\partial_u$, the first prolongation is
$$
\operatorname{pr}^{(1)}V
=V+\left[\eta_x+(\eta_u-\xi_x)u'-\xi_u(u')^2\right]\partial_{u'}.
$$


First prolongation

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

Past exam of the mathematics course of the University of Cambridge / 2017 / ii / Paper 1 / 31A / Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 33A / c / Solution

First prolongation ( $pr^{(1)} V$ )

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First prolongation (pr(1)V)

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