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Answers are given but I am looking solutions on how to derive the given answers. Full solutions is required. I will not pay if the solutions is very short.

Math 242 HW 7 (Sections 3.2 and 3.6) Be sure to carefully justify all of your answers! Section 3.2 Homogeneous equations with constant coefficients Find the general solution to each differential equation. 1. x(6) − 16xjj = 0 2. x(5) + 2xjjj + xj = 0 3. x(4) − 5xjj + 4x = 0 4. x(5) − 5x(4) + xjjj − 5xjj = 0 5. x(5) − 8xjj = 0 1. x(t) = c1 + c2 t + c3 e2t + c4 e−2t c5 cos(2t) + c6 sin(2t) 2. x(t) = c1 + cos(2t) (c2 + c3 t) + sin(2t) (c4 + c5 t) 3. x(t) = c1 et + c2 e−t + c3 e2t + c4 e−2t 4. x(t) = c1 + c2 t + c3 e5t + c4 cos(t) + c5 sin(t) 5. x(t) = c1 + c2 t + c3 e2t + e−t (c4 cos(t√3) + c5 sin(t√3)

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