Find the $ 2n + 1$ characteristic ODEs for the PDE in $\mathbb{R^n}$: $$ x\cdot Du + u^2 = 3|x|^2 $$ I am trying to use the method of characteristics on this non-linear PDE to find the characteristic ODEs but I am having some trouble. I think the part that is tricking me the most is the right hand side because of the $|x|$ ($x$ is a vectors in $\mathbb{R^n}$.
Thank you for the help :)
