Question

Apply the method of undetermined coefficients to find a particular solution to the following system.

Apply the method of undetermined coefficients to find a particular solution to the following system. x' = x - 5y + 4 cos 2t, y' = x - y Xp(t) = 0

Answer 1

Jien that +4cos8t +4 Co8rt G -8 Sina-t 8 SI nt 3 Sing t x"= singO oF ,4x= 4 0s 2t- Sima-t 20 nq differemtiof en y umdetesmiwd Coeficent Aim Now colation Now homo x= d (DLi+) Amiltaif Then Complemeptry dop CtoAxt C&inax Lf gecon ords drtfesentiaf qr Pt) )= 7tt ) Com t) 4000at-SSinat a cospt bsinpt the fom

Оы quяRs, Хр Not elugs nFo arfte plt) A CoAst + B ingt vto differertiap eq plug eh au Nous - 4 A SInst- 4 B Snat 4 to 9t-8&ingt -4ACoost-4Bsinst +4. (Acoo2A + 'Bslng+ O = 4 (0^ 9t-3 &1npt get not next to Noio Our A -43 Sinst ). xp H) -4 A Sinst +4BC083+)+t (-4Aaea^t -4esint fsom A) 4 -t (tcoast +Sinst) -4 g S1n (-4 Asonot4SOADt) +t (-4A cos9t 8&inst 4 toat -4 ASDA 9t +4 B CoBst = 4 (0 9+ -8 Sing t both lde Co pann A 2 4- A=-8 4 B 4

panhulerot Then /. Noo fom ) y X- -5j +4(0A+- ' - 2 R++y& olup Dame prooe from abou e.FCt) tosst tcpsnt of Our Now Plug differentioteq t +4B (08 2t) -t tl-4Aceast -48 Sin at (-4 A s +4t (Aceit+ B<in>t)= 4 cos2t 4 ASIngt t4 B CO22t = 4 (o82t botholde compading -4 A- O A O 4- = 4 Then (1d2 Plt tsint