MHB Derivation of Equation (11) from R Boundary Condition

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http://www.vibsys.put.poznan.pl/journal/2010-24/noga-2.pdf

Equations (9) leads to (11).

How from R boundary condition do we end up with the equation in (11)?
 
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dwsmith said:
http://www.vibsys.put.poznan.pl/journal/2010-24/noga-2.pdf

Equations (9) leads to (11).

How from R boundary condition do we end up with the equation in (11)?

Ok so I figured out what they have done but what does this equation do for them?
 
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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