Question

I AM REALLY STRUGGLING ON THIS PROBLEM PLEASE HELP ME CORRECT AND NEAT WORK IS MUCH APPRECIATED THANKS

(1 point) Find y as a function of t if y" - 8y + 12y = 0, y(0) = 3, y(1) = 9. yt) = Remark: The initial conditions involve values at two points.

Answer 1

G(+) = ? * Y" - By' +12y = 0 , 900)-3 , 9(1)= 9, Find roots of characteristic equation : 72-88 +12 = 0 →! 72-67-2r +32 = 0 8(8-6) 2(8-6)=0 > 8=2,6 82=6 >>: 81=2, 80 The general solution of equation . Y(t) = C, erit + caedet = C, ezt + C2e6t Initial condition y(o)= 3: * 90)= C, e2X0 + Cee 6x0 = 3 →: G + C2 = 3 Second condition y(1) = 9; (1) = Cie? +Cze *: 7.38C, + 403.4 C2 = 9. C, 3.033, C2-0.033 Solution of problem : y = 3.033 e 2t 0.033e bet on Aing. (?) lid) - 2010) - 4,08 110418100