Answer to Question #329795 in Differential Equations for ben

Question

Consider and solve the initial value problem of a new form of life discovered on a distant planet. Outside its habitable zone, the rate of change of population of the life form is governed by the following data: 𝑑𝑦 𝑑𝑥 + 𝑦 = 𝑓(𝑥), 𝑤ℎ𝑒𝑟𝑒 𝑓(𝑥) = { 𝑒 −𝑥 , 0 ≤ 𝑥 < 2 𝑒 𝑥 , 𝑥 ≥ 2 ; 𝑦(0) = 1