What does 2nd ord pde tell you? like fxx(x,y)

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pure and mixed, what do they tell you about a function?
 
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? Exactly what they say- they tell you about how the function, and its first and second derivatives, are related. If not that I don't know what you are looking for.
 
is there a graphical representation of what it looks like?
 
give values to x and y, and draw it.
 
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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