General solution to the euler-cauchy equation

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why does the general solution to the euler-cauchy equation only work for x>0?
 
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It doesn't. It may well work for x< 0. Certainly, because the general equation has a singularity at x= 0, we can't expect a general solution to exist at x= 0 or be extended past x= 0- but you can have solutions that are valid for x> 0 and solutions that are valid for x< 0.
 
ok, that makes sense~ :)
 
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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