It is known that the peak value of a second order system which is excited with a step input can be expressed by
$y(t_p)=1+e^{({-\pi\zeta}/{\sqrt{1-\zeta^2}})}$
In my case, the initial conditions are non-zero. I've solved the differential equation, took its first derivative and then set it to zero, thus got the peak value. But this requires lots of computation time.
Is there a way similar to the one above for non-zero initial conditions case?