Find the general solution of the given system dxdt z dydt

Find the general solution of the given system. dx/dt = z, dy/dt = z, dz/dt = y

Solution

x\'=z

y\'=-z

z\'=y

z\'\'=y\'=-z

z\'\'=-z

So,

z=A sin(t)+B cos(t)

x\'=z

x=- A cos(t)+B sin(t)+C

y\'=-z=-A sin(t)+B cos(t)

y=A cos(t)- B sin(t)+D