# CHEM 110 NIU CHEM110 Practice Exam 3 Key

MATH 336–4 Answers to Exam 3 Fall 2015

Prof. Ammar

1. yp(x) = −1

4x4+ln x

2x4

2. (a) x(t) = −3 cos √3t+1

√3sin √3t, assuming the positive direction is to the right, and

the negative of this if the positive direction is to the left.

(b) C=s28

3,ω0=√3, α=π+ tan−1 −1

3√3!≈2.9515 if positive is to the right, or

α= tan−1 −1

3√3!≈ −0.1901 if positive is to the left.

3. (a) f(t) = e3t3 cos 4t+5

2sin 4t

(b) f(t) = −1

25 e2t+1

25 e−3t+11

5te−3t

4. x(t) = 1

2e−t+e4t−1

2e3t

5. x(t) = −1

18 +1

6t+1

18 e−3t(cos 3t+ 6 sin 3t)

6. F(s) = 1

s2−e−2s

s2−2e−4s

s