Given the equation:
(x^2)y''+xy'-y=0
How do you write this in power series?
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