I have the following first order linear differential equations
$$\dot {z}=z-3t+1$$
$$\dot {t}=z+t-1$$
I have found the unique steady state points as $(z^*,t^*)=(1/2,1/2)$
Now I would like to normalize the system so that the steady-state of the normalized system is at $(0, 0)$.
But I cannot do it properly. Please show me how to solve it.
Thanks a lot