Question

Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. x' = 3x - 4y + sint y' = 2x-y-cost Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. sint sint 10 cost + CA. y(t) = C, e cos 2t + Czesin 2t + 10 -cost 10 9 3 O B. y(t) = C, e - + Cyte -- 10 9 3 cost to sint OD. y(t) = Checos 2t + Cze-tsin 2t + tuto cost + O E. The system is degenerate. OC. y(i)=C7 e'+Cate't ito 3 sint Now find x(t) so that x(t) and the solution for y(t) found in the previous step are a general solution to the system of differential equations. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. x(t) = OB. The system is degenerate.

Help its for my Final Homework

Answer 1

x= 3x - 4y + fint y'=an-y-cost Above equ written as (D-3)2 + 4y = fint where DE Da alert - 27 +(340) y = -cost for eliminating x, equ multiply by 2 and en multiply by (0-3) and Adding Both 2(0-3) +84 = 2 sint -2 (D-3)2 + (0+1) (023) y = – (D-3) cost (041)(0-3) +5] yo asint-(9-3) cost [0²-2D-3 +8]y=2 fint + hint +3 cost [0²-2D+5] Y= zsint & 3 cost Ausiliary Equation m²- 2m+5=0 at 14-go m= 2 + 4i Itzi c.f.= et (c. cosat + Ca sinat Now P.I.= 3 fint + 3 cost D²-2DAS + D²-2D+5 + 3 fint 3 cost D²-2D+S - 3 Sint 3 cost -1-2D+S 1-2D+S 3 fint 308t (-2D+4) 3(-2D-4) fint + 3(-2D-4) cost (-2D+4) (-2D59) (-20+4) (-2D54)

-0-16 t -3 (20+4) fint 3(20+4) cost 4D² – 16 4D2-16 3 (2D+4) Sint 3 (2D+9) cost - 9-16 3 (29+2) Sint 3 (2D to cost 2 (2 cost + 4 fint) + 20 (-2 fint +a cost) cost [+] + fent [4-7] + 3 fint 20 20 1 cost lo y = c.f. + P.I. y = a e cosat + Cal hinatta cost+ 3 fint cosat dy at diff 'y' w.hot. t cet cosat-20, et hinat & Caet finat+alets a fint & 2 cost using in second guen equ all get ax=(c. et cosat-2ciet hinat + Caet fin 2t+26,etcosat - et fint + 270 cost) +(siet c082t + czet sim2t + a cost + 3 fint) + cost (6 +262 +4.) e cosat + (-20, + C2 + (2) et finat +(4+%) fint + (6 + hay cost 11 2x = 2(6 + (2) e cosat + 2 (C2-C.) et hinat - sint 23 cost X (C1+62) e cosat +(C2-C) et sinat - fint t to cost