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 $

$\displaystyle y'(0)=1$

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- Jul 26th 2009, 01:19 PMdiddledabbleFirst Four nonzero terms in power series expansion
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 $

$\displaystyle y'(0)=1$ - Jul 26th 2009, 11:37 PMMoo
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) - Jul 29th 2009, 11:44 AMdiddledabbleWhat about with initial values
Like $\displaystyle y''+(x-2)y'-y=0$

$\displaystyle y(0)=-1$

$\displaystyle y'(0)=0$