Question

Using matrix

For problems 5 and 6, use variation of parameters to find the general solution with A and G given. Alse satisfy the initial value problem.

Answer 1

Given, (1 3 4 -3 -5 7 0 0 -2) (te^-2t te^-2t t^2e^-2t) (6 2 3) from above te^-2t + 0 = 6 -2te^-2t = 6 te^-2t = 6/-2 te^-2t = -3 from the above 3te^-2t - 5te^-2t + 0 = 2 -2te^-2t = 2 te^-2t = -2/2 \r\n te^-2t = -1 from the above, 4te^-2t + 7te^-2t - 2t^2 e^-2t = 3 11e^-2t - 2t^2 e^-2t = 3 11te^-2t - 2(te^-2t) t = 3 now substitute eq r and eq g 11 times -3 -(2 times -3 t = 3 -33 + 6t = 3 6t = 3 + 33 t = 36/3 t = 6 now substitute eq 5 in eq g (11 times (-1)) - (2 times (-1)) t = 3 -11 -2t = 3 -2t = 3 + 1 t = -14/2 = 7