Question

Step by step please.

Solve the system of first-order linear differential equations. (Use C1 and C2 as constants.) Yı' = y1 Y2' = 3y2 (y1(t), yz(t)) = ) x

Answer 1

(1) II 2 y,' y, y z all equations - 3y? as are Un coupled . y, y, 7 こ y, dy.(t) dt 2 ) الان dt 2 en y = t + c g i i - ette e 는 c et - Similarly 3€ 4 = .; d 9(4), 4,(t) 3 = {ciet, Gest

1) 9 y, e 39 4. -333 2 y Y' - 4 94 differential Since a00 equations are un coupled . 19. 391 此 091 =9304 액 y, 5 n yi 2 3A + 3t( 94 34 6 9 - " e

Similarly, 9, - 92 = 94 с, е 444 c, e-3_1 - 90 E Ca e .. { 9,(t), 94(47) , 9, (+) 9,0+) 3 = { е 34 , , e+ () e-14 Cq e - 84