Question

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At least one of the answer (2 points) Find a particular solution to the system of equations x = -224x +96y +91, y = -504x + 216y - 6. Both of your functions must be correct to receive credit. x(t) = (1485/32)^2-(33/4)-(33/20) y(t) (3465/32)^2-(1001/40)+(1603/50)

Answer 1

Q:- dx =-224 x +96 y +9t at dy = -50 4x + 2164 - 6 2 di Differentiate worot. t d²x = -224 dx at 2 at at equation + 96 dy + Now put dy value from equ ® at dex = -224 dx + 96 +96/-50 4x + 2164-6) at dt2 d 2x + 224 at 2 27 dx at = - 48 384x + 207364-576 put y value from egr 0 da at +224 x - gt = 96 y de +224 da at2 at = -48 384x +216 +2248-58 d²x at2 + 224 da at =-48384x+216 dx +4884€- at 1944t

d ²x 녀g디니 at dt 2 ~ 1 +8d Auxilary equation (m²+ 8m) = o a mm+8) =0 m=0,-8 Rt) = se4caeet Now particulas Solution 해 19442 D-8D (3) - (+) 1944 (U+x)= 1+x+x + x 4 금 J1944t 닮을 . 1944t 1999 19 44t 10 & D 10 S 00) 11 1994 - | X1944t 82 2 دع 243 42 243 t 243 6G N C)

Now X(+) = " + xp x (t) = c + C, e8 - 243 +² - 243 ust -8t 243 2 8 64 -ot - - 8e 243t – 243 8 at put all value's in eq' o -8 (₂ e8t 243 t - 243 - ot =-224 C, - 224ce. 8 224 x 22 3+ + 224 X 223 t + 2248 223 +964 2 9 69 +9t -ot 964 = 216C₂ e † 224 G - 2520 - 243 - 112x223+ 8 - 28 X 223 t - 28 X223 ON y = 216 ge 8t + 224 4 252 t - 243 243 – 1|2x 223 8x96 96 96 96 - 288 223 t 28 X 223 -8t Y = se + 236, - 6496 € 50195 - 1511 € 12 96 768 6 50195 -ot 9 e 4 y = +234-223- 1511 +² 768 6

국대 243 t르 2니르 t P 24 3 64 8 ypit 2. ㅓ 51 Lt 203t - 0195 6 3 68