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Question 4: [25 pts] Consider the differential equation y - 4xy = 0. a) Write the general form of the power series solution
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Given differential equwion y – 444 = 0 1e ce y Cx2 = Ean (X-X02} n20 aj يعديد series solwion wround xor o YCX) = Ian (c) di05 (n+3 (n+3)(n+2) 4an ant = no NOLA comparing_both sides ants (n+3) (0+2) - 4 an an+3 (n+3)(n+2) = Han ant3 4an (n+3)(n+2) ncu n? 5. ܙܘ ܢ ܘ } ( L04 16 60 3 ܝܨܬ . 9 ; 6 . ?r E anan ©ܕܠܐ = ao t cu x + arat 93 % +44x4 +4525+ ܐ 5 H {H) - aot aux t arx²+g .. we tuke differentialegn ag SY=0 man (n)(n-1) X 8 Eanx meg 29/12 (n+2) (172-1) xn+2-2 -8E anan=0 no no 2. an +2 (n+2)(n+18 8a4 6.5 (low me 2) 4.32 128 ao 6.5 4 3 2 1 Yox) = Žanx neo - Co tu x + azx?+ 9323+ + 3 ao taux + 8ao x² + 8 al x 3.2 + 16 9

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