Is My Lecturer Correct in Specifying Initial Conditions for PDEs?

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    Lost Plot
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Has my lecturer lost the plot!?

He keeps giving us PDEs to solve where the initial conditions specify x at a POINT rather than along a curve e.g. solve yzx+xzy+z=y given z=2 @ (3,1)


should he not be saying z@ x = ... OR z @ y = ...

thanks
 
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It's the point (3, 1, 2) in cartesian coordinates.
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

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...
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