Hi, it is my understanding that you are trying to solve the system of differential equations in (c) (equation on the above image) using the initial conditions in (d)
The dsolve is incorrectly used with Dx, Dy, Dz terms. The initial conditions Dx, Dy, Dz are incorrectly defined. You may try the following
syms x(t) y(t) z(t) Dx_i Dy_i Dz_i;
Dx_i = diff(x, t);
Dy_i = diff(y, t);
Dz_i = diff(z, t);
cond = [x(0) == 1, y(0) == -1, z(0) == 1, Dx_i(0)==0, Dy_i(0)==0, Dz_i(0)==0];
[x(t), y(t), z(t)] = dsolve([diff(x, t, 2) == 1*diff(x,t) - x - y, diff(y, t, 2) == -x - 1*diff(y,t) - y - 1*diff(z,t), diff(z ,t ,2) == -9*z], cond)
Please refer to the dsolve examples here https://www.mathworks.com/help/symbolic/dsolve.html#bve5m8o-4
