= Solution
A <Lie point symmetry> is a one-parameter transformation of $(x,u)$ which maps the <graph of a function> solving the <differential equation> to another such <graph of a function>, wherever the transformed independent variable is invertible along the <graph of a function>. Its induced transformation on derivatives is the prolongation. Infinitesimally the criterion is $\operatorname{pr}^{(n)}V(\Delta)=0$ on $\Delta=0$. The derivative coefficients can be computed recursively from $\eta^{(0)}=\eta$ by $\eta^{(j)}=D_x\eta^{(j-1)}-u^{(j)}D_x\xi$. This expresses the requirement that the transformed derivatives still satisfy the equation.
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