Frobenius power series repeated roots

John777
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Could someone please explain the y2 solution for repeated roots in Frobenius method where y2=y1lnx+xs \Sigma CnxnI am struggling to figure out how to solve this
 
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For a solution about a regular singular point x=0, look at simplest case first in the form of Euler-Cauchy equation
x^2y''+\alpha xy'+\beta y=0

when the indicial root is a double root.
 
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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