Question

Find the solution to the linear system of differential equations {?′?′==−2?+12?−?+5?{x′=−2x+12yy′=−x+5y   satisfying the initial conditions ?(0)=1x(0)=1 and ?(0)=0y(0)=0.

د (1 point) Find the solution to the linear system of differential equations { -2x + 12y -x + 5y satisfying the initial conditions x(0) = 1 y د and y(0) = 0. x(t) = yt) =

Answer 1

a x = -2x+12y = -x +57 :! b y(0) da dut +2) 4-12y=0 De -2x +12y DY -x+s4 + x + (0-50y-0' -> x +2) O+ 2)2-12y = 0 +2) * t (D+27(0-5) = 0 - [60+27(0-5) 4+12y] =0 y [ 09.30-10412]=0 y can't be zero so => 77 2,1 77?3.7+2=0 0-30.+2=0 Auscially equation yets=ce at the from y's - X+5y x=sy-y' = 54 - DY Dy = + get .. x= Brie2t+ s[62247514] - [zcieet cet x(1):3622474 Çzet 26 le CamScann

Criven ecol=1 yo) 3C tug CtQ =) K,=-62 30-uci fcia-1 (221 - x(t) = 25 -3e tuet - ezt tet CS 9(t) = Scanned with CamScanner