Let A be a constant matrix. Suppose u(t) solves the inital value problem $\dot u = Au$, $u(0) = b$. Prove that the solution to the inital value problem $\dot u = Au$, $u(t_0) = b$ is equal to $\hat u = u(t -t_0)$. How are the solution trajectories related?
I am not good with proofs. Never have I done it before prior of taking this differential equation class. Can anyone show me how to prove this?