I have a homework but cannot solve it. I Cannot found useful information about my current topic.
Construct a 3rd order linear system and create a state equation. Two roots must be complex. one root must be a real number. apply 2 * cos(t) + t + 1 function to solve. First condition would be as desired.
Please help me :( Any help is appreciated.
I found these website about second order functions: https://apmonitor.com/pdc/index.php/Main/SecondOrderSystems
If the given function is to be a solution of the equation to be constructed, you could select the characteristic roots to be $\pm i$ for the cosine term and $1$ for the arbitrary real root. Then $$ (D-1)(D^2+1)f(t)=(D-1)(t+1)=-t $$ so that $f$ is a solution for $$ f'''(t)-f''(t)+f'(t)-f(t)=-t $$