Question

how do i find the two power series solutions of y"-2y'+y=0

Answer 1

you assume:
\[y=\sum_{k=0}^{\infty}A _{k}x^{k+r}\]

Answer 2

now differentiate it for y' and y''
and plug it into the equation.

Answer 3

Could you please clarify the method in steps. Thanks.

Answer 4

so i wrote what is y.
now for y':
\[y' = \sum_{k=0}^{\infty}(k+r)A _{k}x ^{k+r-1}\]

Answer 5

take another derivative and you get y''
then plug all the 3 into the equation

Answer 6

About which point? \(x=0\) ?