I am applying at a Faculty for Electrical Engineering, and I have an entrance exam in two days. I have few exams for exercise, from previous years and I keep getting stuck in one particular type of problem:
"A dynamicaI system is described by a differential equation of the following form: $$y''(t) + 5y'(t)+4y(t) = u(t)$$ where t is the independent variable of time, $u(t)$ is the input signal into the system, and $y(t)$ is the system response."
I need to prove that if the system is excited with stepped amplitude signal of $1$, the output of the system in the steady state will reach a constant value of $0.25$.
Can anyone please suggest how can I solve this problem. I think I should use Laplace Transformation to solve it, but I do not know to how transform the above differential equation in some type that can be solved with Laplace. Also, i do not get where does the amplitude signal of $1$ is used.
Any help or hints are welcomed and appreciated, I need all the help I can get. Thank you.