English: Now, similarly if I have a exponential s t as the input when p 1 and p 2 are complex conjugates of each other and I will assume that s is not equal to either p 1 or p 2 we will simply get + exponential s t. And similarly, if the p 1 and p 2 are real and identical, but s is not equal to p 1 we will simply get + exponential s t, but these are not the only possibilities for instance, in this case I could have s equals p 1 or s Similarly, if s equals p 2 we will have this coefficient of t multiplying exponential p 2 t. And similarly, in this case in the second case p 1 and p 2 are all of the identical if s happens to be equal to p 1 then we will get A 1 + A 2 t + A 3 t square exponential p 1 t. So, we get t square turn as well and finally, in this case it is possible that s is equal to either p 1 or p 2 and again we have the same cases here, we could get A 1 + A 2 t exponential p 1 t + A 2 exponential p 2 t and so on.
Telugu: అదేవిధంగా, p ₁ మరియు p ₂ రియల్ మరియు సారూప్యమైనవి (Identical) అయితే, s = p ₁ కి సమానం కాకపోతే మనకు + e^(st) లభిస్తుంది, అయితే ఇవి ఉదాహరణకి మాత్రమే అవకాశాలు కావు, ఈ సందర్భంలో మనం s = p ₁ లేదా s = p ₂. కాబట్టి, s = p ₁ కి సమానం అయితే మనకు A ₁ + A₃ t × e^(p)1^(t)+ e^(p)2^(t) లభిస్తుంది.