# Solving PDE only using method of characteristics

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.