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# Problem #7: Considcr thc diffcrcntial cquation [15 marks] 4xy" + (2+x)y'-y = 0.Without solving this diffcrential cquation, onc can say that any powcr scri...

## Question

###### Problem #7: Considcr thc diffcrcntial cquation [15 marks] 4xy" + (2+x)y'-y = 0.Without solving this diffcrential cquation, onc can say that any powcr scrics solution centcrcd at thc ordinary point xo 5 (i.c_ scrics involving powers of x 5) has radius of convcrgcncc at lcast cqual to R. What is R? (Entcr infinity if R ~,)Find the two roots of the indicial equation associated with the regular singular point Xo 0. Scparatc your answcrs with comma_ (c) If r1 denotes thc largcst of the 2 ro

Problem #7: Considcr thc diffcrcntial cquation [15 marks] 4xy" + (2+x)y'-y = 0. Without solving this diffcrential cquation, onc can say that any powcr scrics solution centcrcd at thc ordinary point xo 5 (i.c_ scrics involving powers of x 5) has radius of convcrgcncc at lcast cqual to R. What is R? (Entcr infinity if R ~,) Find the two roots of the indicial equation associated with the regular singular point Xo 0. Scparatc your answcrs with comma_ (c) If r1 denotes thc largcst of the 2 roots of thc indicial cquation, the diffcrential cquation above has solution of thc form Cnxn+n n=0 Whcrc g(n)cn-1, n 2 1, for certain function g(n). Compute g(n). Writc thc sum of thc first non-zCrO tcrms of the scrics in (c) if c0 = 1. What is the radius of convcrgence of the scrics in (c) if c0 12 (Enter infinity ifit is infinite.) Enter your answer symbolically, as these exampes Problem #7(a): Enter your answer symbolically, these examples Problem /7(b): Enter your answer a5 symbolic function of n, as in these examples Problem #7(c):

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