Question

0 of the differential equation (1 point) Find the indicated coefficients of the power series solution about x = У' — (sin x)y У(0) %3D —9, У (0) 3 —3 =COS X x2+ у%3 —9 — 3х+ x4O(x5)

Answer 1

suahion gCsinz)y Giuem difaranhial ty(e)- Differn tiahng t d Stur Sin(x) yCosk y-sinx Agai olifnahiahg (-Sina ySin ()y- Ce()Y P 74) gedSiny7 -a CafX Cas (x)Sin( +Sin - (y 41 y (X) fr - Sin (x) g 2 Ca 0 y+ Sin (x) y=-Ca

ygiuesy fosinoto yCo) -O x(-9) gite sy giwy yo)-since)y(e)-Ces(o)y(o) -Sing -1X(-9) 4) * STno 2O)yto +Sinyto C4) 4 - o-2XIX(-3) to - 4) +6 4) = -7

Now peuur Sriaaf diftarental i1 4- 3 Ylo)tyo t 2! 4[ 3! il +0() (-9) 7) 24 (-3) 2. x3 + 24 -9 + +otx) -3 4 -9-3 x + 2 24 2.