Question

(1 point) Find the solution to the linear system of differential equations -7 + 154 - 6x +12y satisfying the initial conditions (0) - 7 and y(0) - 4. y(t)

Answer 1

n'= -72 +15 y = of u and y' 5.xl → y' -6n +12 - +12y Differentiating with respect to x of 0 20" -zul + 15 yl -7(-1.1154 ) +156 62 +24) [putting the values -412445 – 416..+5 ( '+7) [from O] -6.x u! 50'+60=0 7 (DP-50+.6)a=0 Where D= The auxiliary equation in .-5m+6=0 -> (m-2) (m: 3) = 0 i = m = 2,3 The general solution in alt) = A e2t +Bet Putting n(t) in 0 and We have 15y = x+7= 2ne2t +3Bet ta be?t: +7 Best =9 A 12 + 10 Be 36 2 Best 3 d2 atz 3 Y(4)= 3A 5 @? + 14

Now and 28. + 5 3 n(0)=7 A+B=7 (from y (0)=4 => 31 =4[from © Solving these two, we have A= 10, B = -3 ... r(t)= 10e 6e2t_2eßt 10024 -3e3t and y(t) Il