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--> Find a power series solution for y''(x) - y(x)=0

First i attempted to find singular and ordinary points for the differential equation and i found that x=0 is an ordinary point. then i set y=[tex]\sum[/tex]A(n)x^n for n=0 to infinity

subsituted into the differential equation after finding the second derivative.

then after some manipulations i found that

y=A(0)[tex]\sum[/tex]x^(2n)/(2n)! + A(1)[tex]\sum[/tex]x^(2n+1)/(2n+1)!

the solution says it is equal to e^x+e^(-x)

I tried using the series of e^x=[tex]\sum[/tex]x^n/n! but i couldn't get the solution

help people

THANKS