|Nov22-06, 12:40 AM||#1|
classifying ordinary and singular points
I am stuck on classifying the points with this DE...=\
The solution says (sin x)/x is infinitely differentiable...so x=0 is an ordinary point?
I was taught...if P(xo)=0, then xo is a singular point. Here P(x)=x...so x=0. So, what I don't get is the "infintely differentiable" part. Does it have something to do with the convergent Tayloe Series about x=0? And what does that mean?
I got another example here...
Here P(x)=0 so x=0 is a singular point. It's also a irregular singular point because as x->0 (cos x)/x goes to infinity. How come here x=0 is a singular point here?
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