Question

d1 dy 2. Solve the system dt dt2 da dt =t = 2 dy (25pts) + 3x + + 3y = dt

Answer 1

7 2 22 att Elemi two, we have + D given Doe's can be written as px DY (whene D = af et (OD +3) x + ( +3) y = 2 2) minating y from there [P" (D+3) (D+3)] (0+3)t + D. 2 D(D+1) (0+3)x auxi marry equ" is m(m +1) Com +3) =0 =) m=0,-1,-3 so its complementary function is = c + czet exslaitz being arobiprony constants particular integral =) 1 +3t So ots 20 est where so its - 1+37) D (D*+40+3) 1) (६ 3 1 i/ 3D to Ci+ 40+5)*(1+3+) so (- 10+0) C1+3+) so (1+3+ - 4.3) ( 34 - 3) 1 s 3D as 3D t 2 So ats general sol" is e(t) = citeet +₂ e 3t rt 2

from hone x+y 2 D43 (1 + $12 3 (1-1).2 WIN = ) 11 کا WIN ..,- ez etacjest _ t + + + 2 3 y