Question

X 8.3.15 Question Help Find at least the first four nonzero terms in a power series expansion about x = 0 for a general solution to the given differential equation. y"' + (x + 10)y' +y=0 y(x) = + (Type an expression in terms of a, and aq that includes all terms up to order 3.)

DIFFERENTIAL EQUATIONS / Linear Algebra

Only people that are proficient in DIFFERENTIAL EQUATIONS should even attempt to solve. No beginners or amateurs allowed.

Please write clearly and legibly. No sloppy Handwriting. I must be able to clearly and easily read your solution and answer.

Circle final answer.

Here is an example of what the answer should look like. They should look practically identical really.

example

Answer 1

Solutions yt (melody+y=0 at n=0 y (a) = { ana no nal y'(x) = nanant 9"()= în(n-1) Am 21-2 n=2 put all these values in the differential egyation Z ncn-san 2-2 '+(a+10) Enanan-i te anal=0 1=2 nal no En(n-11 an 20-2+ nanda +10% nanana + 8 anal=0 n=2 nal 121 ho {(1+2)(n+1) An +22² + 8 nana" + 108 (n+1) antant & anx"=0 n-0 no n=0 n=1 og s 2.1.ą + {{n+2)(n+1) antz x + E nana +10.1.a Hoke into ante" nal 1-1 + Eanan tao O nal 202 +0 a + ao + 2 [n+2) (n.) antz + na po tanti anti + an Iar- 20₂ + loa taotq 9 (0-22(64244 in+2)(n+7 Ant2 + (n +1) An + (nen Anth 3 x=0 comparing (n +2) CnH) Ant2 + (+9an +In+1) 2.0 (1+2) antz +an + anti=o ant2= = an toanal Th+2) antza -an-10 anos (n +2) a ² -109, ao

for nos 0₂= -Q-1002 Az = -all - 10 a a. 10 3 3 Ĉ-- [-1001 loa - do ay + 50 a tha 3 3 az = 49 + 2 Sao Sg Now y (2) = { anda y(a) 2 Yia) 20 +22.+ az t@,x+ = do +248 +f-109,60 73*+ [420 7 5 ]2+ = 0o 90 32 uşaq xe + Qx-1043* + 420, 42 You [***]-[2-14] you 300 (20.7*]+91[1-5** ****] 3