Where Did the R's Come From in the Transport Phenomenon Problem?

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i got this from my notws and i just can't seem to figure out how the second step is obtained? can someone explain to me where the where r's in the numerator came from on the second line when dividing by the volume of the shell?
 

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That is the original r from the previous equation.
 
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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