Question

The power series solution of the Initial-Value Problem (IVP) (x² + 1)yl + xy + 2xy = 0 y(0) = 2 is given by y(0) = 3 4 13 325 2 y=2(1 + + :). 2 + + 3 20 6 2 2125 y= 2 + 3x + +. 6 2 4 23 3.25 y = 32 =3(< + + -) +2 (1 + + :) 3 20 6 2 7.23 21.25 y= 2 + x + + + +... 6 2 4 None them

Answer 1

The coefficient of at Solution, (х+1) y" + xy + 2х9 го Эм законод, а,с») y = at 09' + схуго О, (2) = 1+1 o, Co ) = 1 + b = = os an odinoxy Point. Now, Using Power Series Method Assume 9x) = x , со + 4х +с, х*+, х'. Каб у'см) - С + С. (2х) + c 3х2) т. 9" (%) - 2С, +6 C(x) +2-44 (x+) + 20L, х, from ea (+10 (1.4. + 6 ч 12. де зо, 23.-] *[c C4 + 2C, X + 3 x2 + 4+4 х? + --] + 2x[ + 4х+ Сах* + ** ----] =o The coefficient of no ПС, 2 O С, 20 6 са + Cu + 2C, во The coellicient of ² 12C4 +4, +2C + 24 = 0 - С1

The Coefficient of ² 2006 + 6 (3 +363 + 2 = 0 =) (CG from 663 +4 + 2lo=0 2-9 (3 20 & Ca = - 444 €3+ Co = CA (1 2 – 663 - 200 y cu) z lot Gut Cu²+ C3 2² +4 47 +425 + - Yea) Lo + (-663-260) u + 0x2? + (z 4² + (6 + Co) at + (- 9 (3) 45 you) - Co[2 -2x + 2) + [-62 +23+3+* - 2.28] y' (2) co [-2 + 4 w3] + (3[-6 + 322 +423 - 45 xt] 20

B 03-2 2 C[I] +5C0) 2 y'0) = 3 3= C[2] +50) 6 = 2 3 -4 -65 0 5 6 yu) = 21 - 2x + 1 ] + (-) [-X + x + -2 x6] 2- 47 t르 24 +7 아구지 좋지고 콩지 집 yu = 2+37 거3 쪽 구린 35 3 2 나이 a None of them