Question

(1 – x?)y –y=0 Assume solution takes the form y= Enzo any” a. find the recursion for An b. Given that Ao=2,A1=0, find A2 & A

also find the radius of convergence

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Answer #1

g= Ź an z* >y- Šnanzas no 1-2 = n(n-1) an 2-2 n2 for n20&n=) termes are o 2 (1-2)=6 > y = (-)6-2+) 06.02** -Ž (n+2)(WH) anaz(2²+3n+2) Qnrz-(27-n+1) an=0 Ant 2 = 22-nth an N²+3n+2 90=2 id=Oot2 = 8 oth a +? O*+30)42 = + (2) = 1 0,=0 as 1+2 - 2+3 (1)+mes 7. [2m) - (2m) 71 x ² cl tim (2m) + 3 (2m) +217 x²</ → 1x1 <1 - 1<x<1 8. radius of convergence=1

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