Find the first Four nonzero terms in power series expansion about x=0
$\displaystyle y'-y=0$
or
$\displaystyle y''-2y'+y=0$
For an initial value system $\displaystyle (x^{2}-x+1)y''-y'-y=0$
$\displaystyle y(0)=0 $
$\displaystyle y'(0)=1$
Find the first Four nonzero terms in power series expansion about x=0
$\displaystyle y'-y=0$
or
$\displaystyle y''-2y'+y=0$
For an initial value system $\displaystyle (x^{2}-x+1)y''-y'-y=0$
$\displaystyle y(0)=0 $
$\displaystyle y'(0)=1$
Hello,
Consider the power series expansion of the solution (in any equation)
$\displaystyle y=\sum_{n\geq 0} a_nx^n$
Then $\displaystyle y'=\sum_{n\geq 1} n \cdot a_nx^{n-1}$
etc...
Then find a recursive relation between $\displaystyle a_n$ and $\displaystyle a_{n-1}$ (or possibly $\displaystyle a_{n-2}$, 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)