Question

Part B please!

Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. x' = 9x - 10y + sint y' = 5x -y-cost Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. 51 O A. y(t) = C, e -41 cos 5t + Cge -41 sin 5t + no cost + 200 sint O B. y(t) =C, e4+ Czte 4 + 2 cost+ 206 sint OC. y()=C1 e - 4t +Cyte - 4 + 208 cost+ 208 sint D. y() = C1 e *t cos 5* +Cz e* sin 5t + 2 cost + 20€ sint O E. The system is degenerate. 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.

Answer 1

K-91-LOy + Sit 0. y' = 54 - y - Cost - Now already, we have y(t) = Ceut const + Ce esimst + She cost- + 21 20. Sint Now. y(t) = (hettcast-Sellt sin st) +63(4e4tsiun St +5e4tcast) - sunt + 20. Cat puting in . we get 5x = y'45+ Cost =(4e4tes st-setts in St + ettersst) + C2 (4e "tsinst useft const telesunst) (b +1 ) Cost of 2016 süst = 5e,ſentoonst - et sin st) + sez(e4t erst test sim st) + 200 cost sint + X(t) = 9(elltcois St-ellt sin st) tez (eut cast tellt sin st) + soon Cost - web simt a. M(t) = (9,+)euters st +(2-8, Deutsinst + in Cost - 2 sunt