sk 14. Find the general solution of the following homogeneous system (8 Puan) 3 2e5 =...
14. Find the general solution of the following homogeneous system * (8 Puan) [29 X' х teze si x=ce [1] [2] =ce [1] + [2 U] X = cje! O X = ge! + Cest none of these X = cie X=3
2 8. (10 points) Find the general solution to the homogeneous system of DE: | 3 x' = Ax where A = -2 1 - 1 -2 -4.
1 -2 Find the general solution to the homogeneous system of DE: 3 2 6 x' = Ax where A = -2 1 -2
7. (10 points) Find the general solution to the homogeneous system of DE: -1 x' = Ax where A -2 = [ 21
Find the general solution for the given non-homogeneous system of DEs. 7-8t2 - 160 - 25 X' = (3 2) x + (-712 – 134 – 23)
7. (10 points) Find the general solution to the homogeneous system of DE: x' = Ax where A = [-2 21
Verify that the given vector is the general solution of the corresponding homogeneous system, and then solve the nonhomogeneous system. Assume that t> 0. bx' = (36 - 16)* +(8524->), x) = 41(2)-3 + c3(3):46 10 = C(1,2)=8+ C,(2,1)e46 +24-3,) + +(2,0) + +15(0,1%) + 234 3:0) +2=23/0,33) 15 X(t) = + + 7
Find the general solution to the non-homogeneous system of DE: -4 X+
8. Determine the appropriate form of the particular solution for the following non-homogeneous linear differential equation with constant coefficients. (8 Puan y(4) +9y" = 5+ &'(x-3) + 4sin (3x). none of these O Ar? + Bx cos(3x) + Cx sin(3x) + De' + Exet Ar + B + C sin(3x) + D cos(3x) + Exe" A + Bre-3x + Crer + De + Exet O Ar? + Bxe- + Crex + Det + Exe! A + B sin(3x) + Cxsin(3x)...
Find the general solution to the linear system of non-homogeneous differential equations x = x + x + 1 xz' = 3x1 - x2 +t