Let be the soloution of that is defined in the whole plane. Prove that .
Hint: Think of the characteristic curves of this PDE.
HOPE You'll be able to help me
Thanks in advance!
It is one of the characteristics though. The constant c_1 is the slope and will vary along each characteristic, while being (explicitly) determined by c_1=y/x. So at x=0 (for which y=0) the slope will become infinite and the solution will develop a shock. check your notes.