Solve $aU_x+bU_y+cU$=0 using characteristic method. I know how to solve this by change of coordinates as in this article.
But without changing coordinates how to do it with the method of characteristics? I know how to solve if it was $aU_x+bU_y=0 $by using directional derivative.
Also in page 10 of that article they have used Jacobian.Please explain why Jacobian is used there.