[SOLVED] Steady state solution I was wondering if I did this question correctly, solving for y(t) and putting t = infinity to get a steady state solution. Or is this wrong or is there an alternative way that is much quicker (as solving for y(t) would take a page of working, where the working out on the exam paper was less then half a page) 1. The problem statement, all variables and given/known data A continuous linear time invariant system with input x(t) and output y(t) related by: y''(t) + y'(t) - 2y(t) = x(t) Find the stead state output of the system for x(t) = 2cos(t) + sin(200t) 3. The attempt at a solution Initially used laplace transform to get Y(s) and inverse transform and put t = infinity to see what part died out over time (transient reponse), however it did not seem correct (used mathematica to double check) as I got a e^t term. Using ODE solving methods with characteristic equation r^2 + r - 2 = 0, I solved initially the homogeneous solution which had a Ce^t term and got a similar total solution to when using laplace transforms.