Question

Done Homework 5.2 Score: 4.5/7 4/7 answered 6 VOO Question 5 < 0.5/1 pt 52 98 Details Solve y” – 2y' + 2y = 0, y(0) = -1, y'(0) = 3 g(t) = The behavior of the solutions are: Oscillating with increasing amplitude Steady oscillation Oscillating with decreasing amplitude

Answer 1

The characterstic equation for 2. le y" - 2y + 2y = 0 -2a +2=0 a= 2 + V62)2 – 4(1)(2) a 2 at ry = at2i at 2 2 So, et cc, cost tęsint) y'= et l-e, sint + Ccast) + e* Cc, cost tosint) y Co) = = e cc, casot Esiho) = -1 2) Ice, to) =~1 s G=-1. y'Co) = e C-c, sin ot Goso) te C.C, caso ta sho) = 3 G te=3 G 3-4,6 = 3-0 =4 so y = et c-Cost ty sint) The behaviour of solution are oscillating with increasing amplitude (due to presence of et ? pleave uprote!!)