# Math Help - First Four nonzero terms in power series expansion

1. ## First Four nonzero terms in power series expansion

Find the first Four nonzero terms in power series expansion about x=0

$y'-y=0$

or

$y''-2y'+y=0$

For an initial value system $(x^{2}-x+1)y''-y'-y=0$
$y(0)=0$
$y'(0)=1$

2. Hello,

Consider the power series expansion of the solution (in any equation)

$y=\sum_{n\geq 0} a_nx^n$

Then $y'=\sum_{n\geq 1} n \cdot a_nx^{n-1}$

etc...

Then find a recursive relation between $a_n$ and $a_{n-1}$ (or possibly $a_{n-2}$, for the last equation)

See here for an example : http://www.mathhelpforum.com/math-he...s-problem.html (take care of the steps, that's all)

3. ## What about with initial values

Like $y''+(x-2)y'-y=0$
$y(0)=-1$
$y'(0)=0$