Question

Show Timer Question Completion Status: To find a particular solution of the differential equation (D - 1)?(D – 2)(D? +1)y = f* + COS I — 2 sin one can use the following trial solution On Aox?e* + 3(Al cos 3 + A2 sin 2) OB Aoxe + .(ACOS T: + Asin x) Oc Anx?et + x² (A, COS I + A, sin x) OD Ao + Au cos x + A, sin x O Age* + (A, cos x + A2 sin x) Chicksaw and submit to me and satenie. Click Save All Answers to all our

Answer 1

Arswes ir since given differential equation (DE) (0-1)²(D-2) (0²4)y=e" + cool-gsina its ausilicony eqr D= mn (may?(mag) (m²+1)=0 => [m-v=o, magro, m?+1=0 m=1,1, 2, I so its tricu solution or cf is 221 CF=(4 +6%) e a te + cu sinxt scosse

Now general solution of eroberential equ i y (a)= CFAPI where PI is the particular solution NOW (ed f cooxe asina) T PI (D-1,2D-2)(8+1) e a (cox-gsime) + (6-1)²(D-2) Co²+1 (D-140-2)CD?+1) eau it fra) to pan fca) FCD) of fea)=0 ten f(0) =(D-aja prol (we com write) aa e tren 921 - in (Dragi and for singa or Coane sinan = sinan de frra2) to f(D? fla92) (-)" an sin (ax tn) sincra = (207" in (1²7 of it is orale same for cason

do PI = ea it D-1 (1-2)(1+V frosa-ssinae) 02-8071 (0-2) (0270 - = (cosx-asina) 2D (0-2) 62+1) 2(D-12 D(0-2) =D² 2D = 2² 22 pa 2 26-1-20) (04/case-asino) (cosa adina) = R. a e 4 + (1-20) 2 (1+20)(1-2 DJ (D?+1) xen [cos i-agine-a (=s.ex.-2.com)] こ + 2(1-403) (D2+ [scour) Ded -a²en ot { dae 4 201-403)(0271 S coon x?e? = + 4 211+4)(04111 2 ? Col3+C) E-sina 2.21 ((x+mo) x 1.()' & ul d (2.1)' 4 (PI= -aea1 + x sina q

: (GtGalea & Gent 2 e x sinx + & brows