Given the equation:

(x^2)y''+xy'-y=0

How do you write this in power series?

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- Dec 8th 2009, 07:02 PMToucanWriting a differential equation in power series
Given the equation:

(x^2)y''+xy'-y=0

How do you write this in power series? - Dec 8th 2009, 08:30 PMProve It
- Dec 9th 2009, 02:48 AMchisigma
The DE equation ...

(1)

... belongs to a family which is called 'Euler's equation' and its particular solutions are of the form . Substituting in (1) we obtain that it must be...

(2)

... so that ther general solution of (1) is...

(3)

... which is itself a Laurent series expansion...

Kind regards