Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3 / 32C / c / i / Solution

When $f=0$, each identity ${\mathrm{pr}}^{(3)}{V}_i(S)=c_{i}S$ vanishes on the equation. The equation $S[u]=0$ has all three infinitesimal symmetries $V_1,V_2,V_3$. They generate the projective transformations of the independent variable.