Mathematical Physics: Bessel functions of the first kind property

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I ran into some formula:

^{a}_{0}∫J_{o}(kr) rdr= a/k J_{1}(ka)

How can this be true? What property was used?
 
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Try writing down the series representation of J_0(kr) and integrate term by term.
 
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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