Toronto Math Forum

$x^2 - y^2 = C$ is a hyperbolic curve so it has two parts for x. I see now, thank you professor.

Chapter 2.2 problem 2 equation (9): $u_t + yu_x + xu_y = x$
and we get $\frac{dt}{1} = \frac{dx}{y} = \frac{dy}{x} = \frac{du}{x}$
By solving $\frac{dx}{y} = \frac{dy}{x}$ first we get $C = x^2 - y^2$
But we solving for either $\frac{dt}{1} = \frac{dx}{y}$ or $\frac{dt}{1} = \frac{dy}{x}$ we need to substitute $x$ for $y$ or the other direction, so in this case we will have a square root function like $x = \pm \sqrt{y^2 + C}$
I am not entirely sure whether or not we should proceed with the $\pm$ sign here or is there another easier approach to this question?

Then your best shot would be

• either to ask during Prof Kennedy's Office hours
• or to formulate the problem and define everything  (that is $u, v, S, \tilde{S}$) here by yourself without screenshots 

My guess that it is a continuity condition.

Hi Professor Ivrii, this comes from Christopher's lecture #3 when he discussed transport equation, directly from his lecture notes #3 on top of page 2 : )

Can anyone help me check the answer? Thanks

(1) linear-homogeneous
(2) Quasi-linear
(3) Semi-linear
(4)Quasi-linear
(5) Semi-linear
(6)Quasi-linear
(7)Quasi-linear
( Semi-linear
(9)Quasi-linear
(10) Quasi-linear