Question

Yă =-6 Ye + 2 2 ya + Geet In this section, we're interested in systems of linear differential equations, like this: = * That says that y_l's derivative (slope) is determined by the values of y_1 and y_2 (at any specific x) and y_2's derivative is determined by those values as well. In linear algebra notation, we can write that system as Y 15 -3 Y LY 2 Pre-class exercise 2. Verify that C, ex Ya ac, é solves the system (X 1 ca e 8

Answer 1

Ginen system of differensial Eqn as y,' = 54,-342 ya = -6%,+2Y2 Arranging matha form Yo in 5 - 3 Y لا 2 6 %3D 3 Benote da Eqh =) DY, = 54,-342 -) (0-5) 4, + 3 Y2 - 0 Eq" @ =) DY2=-64, +2Y2 3) 6 Y, +(0-2) Y2 - 0 4 Multiple eq" by (0-2) of eqng me get Ey =) (0-2)(0-537, +3 (0-2342-0 Egz-) 184, +300-2) Y2 = 0 subtracting eqr ① s me get Бу 3 8

2 (10-2) (0-5) -183 y, = 0 =) (03-50-2D +10-18 )y, -0 =) CO-70-8) Y, = 0 © of eam is m² fm.8=0 M-8) (m+i)=0 Auseilary eqn -) 13 -1 s m=8 Hence 8x 3 me get. a Yi (s): ce tree Using in ear olcettlese)- 5 ) - 5 (ceafleppey +372 = 0 A) -e, é* + 862 18* - 56,6*_52288 +372=0 =) 392-60, ex Y2 = 2C, 892 e8x + 3₂ e