I have been thinking about this, would I have to define:
<br />
C=\frac{\partial}{\partial x}\int Cdx<br />
and then define
<br />
B'=B-\int Cdx<br />
to get
<br />
\frac{\partial A}{\partial t}+\frac{\partial B'}{\partial x}=0<br />
and then apply Lax-Wendroff to the above equation?
I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...