Question

Section 3.4 Repeated Roots: Problem 1 Previous Problem Problem List Next Problem (1 point) Find the general solution to the homogeneous differential equation. 2 dt dt Use ci and c2 in your answer to denote arbitrary constants, and enter them as c1 and C2. y(t) - (formulas) iii help

Answer 1

d^2y/dt^2 -8 dy/dt + 16y = 0 It is a second order linear homogenous differential equation with coefficient let y = e^mx is a solution implies e^mx(m^2 -8 m t + 16) = 0 (e^mx notequalto 0) implies (m -4)^2 = 0 implies m = 4, 4 So, since for repeated roots y = (c_1 + c_2 x) e^4x