MATH 2341 Exam 1 | Full Questions and worked Out Solutions | 2026 Updated | 100% Correct - Northeastern University.

MATH 2341 FINAL EXAM (VERSION A) SPRING 2026


NAME________________________________________ April 25, 2026


YOUR INSTRUCTOR (Circle Your Section):

George Hoffman Lang Lupi Tzigantchev Wilson

9:15 9:15

10:30 10:30

1:35




SHOW ALL WORK. ANSWERS DIRECTLY FROM YOUR CALCULATOR WILL RECEIVE
NO CREDIT.


Part One: _____ (out of 22 points)


Part Two: _____ (problem 12 out of 9 points)

_____ (problem 13 out of 11 points)

_____ (problem 14 out of 14 points)

_____ (problem 15 out of 10 points)

_____ (problem 16 out of 12 points)

______ (problem 17 out of 10 points)

______ (problem 18 out of 12 points)



TOTAL: ______ (out of 100 points)

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PART ONE: Multiple Choice (2 points each)

Be careful as you work through these problems as there is no partial credit.

1 A tank contains 15 liters of water in which is dissolved 1.5 grams per liter of a certain chemical. A solution of 2
g/L of the chemical flows into the tank at the rate of 9 liters per minute and the well-stirred mixture flows out at
the rate of 6 liters per minute.
If A = A(t), represents the number of grams of the chemical in the tank at time t, which of the following initial
value problems best models this situation ?
2𝐴 2𝐴 𝐴
(A) A′ = 18 - , A(0) = 22.5 (B) A′ = 18 - , A(0) = 22.5 (C) A′ = 18 - , A(0) = 22.5
5−𝑡 5+𝑡 5+𝑡

𝐴 2𝐴
(D) A′ = 18 - , A(0) = 22.5 (E) A′ = 18 - , A(0) = 1.5 (F) None of these
5−𝑡 5+𝑡



Answer: ______



2 Which of the following differential equations is/are NOT separable ? Here y′ = dy/dx.

(A) x3 y′ = y + x3 (B) x3 y′ = y3 (x + 1) (C) y′ = 6 + 7x (D) y′ = y2 sin x + 4y2

(E) B and C are not separable (F) B, C, and D are not separable (G) All are separable

(H) None are separable

Answer: ______




3 A 4 × 4 matrix M has characteristic equation (λ – 3)2 (λ + 1) (λ - k) = 0, where k is unknown. If det M = 18,
what is the value of k ?

(A) k = -2 (B) k = 1 (C) k=2 (D) k=3 (E) k=4 (F) None of these

Answer: ______



4 Which of the following functions is the inverse Laplace transform of F(s) = 21e-5s ?
2
s - 8s + 25

(A) 21 u(t -5) e4(t -5) cos 3(t – 5) (B) 7 u(t -5) e4(t -5) sin 3(t – 5) (C) 21 u(t -5) e4(t -5) sin 3(t – 5)
(D) 7 u(t -5) e4(t -5) cos 3(t – 5) (E) 21 δ(t -5) e4(t -5) sin 3(t – 5) (F) 7 δ(t -5) e4(t -5) sin 3(t – 5)
(G) None of these


Answer: ______

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5 For what value(s) of c will the spring-mass system 5/16 xʹʹ + cxʹ + 5x = 0 have overdamped motion ?

(A) c = 5/2 (B) c < 5/2 (C) c > 5/2 (D) -5/2 < c < 0 (E) 0 ≤ c < 5/2
(F) None of these


Answer: ______



2−𝑥
6 Which of the following is an integrating factor to the equation y′ + y = xex ?
𝑥

(A) x2 + e-x (B) x2 - e-x (C) 2xe-x (D) 2x + e-x (E) x2e-x (F) None of these


Answer: ______




0, 0≤𝑡<2
7 Which of the following is the Laplace transform of the piece-wise function f(t) = { 2 ?
𝑡 − 4𝑡 + 4, 𝑡≥2

𝑒 −2𝑠 2 4 4 2𝑒 −2𝑠 4 𝑒 −2𝑠 2𝑒 −2𝑠
(A) (B) e-2s ( - + ) (C) + (D) (E) (F) None of these
(𝑠−2)3 𝑠3 𝑠2 𝑠 𝑠3 𝑠2 𝑠3 𝑠3




Answer: ______



1 2 𝑘
8 For which value(s) of k is matrix A = [0 1 2] invertible ?
𝑘 2 1

(A) All k except 2 and 3 (B) All k except 0, 1 and 3 (C) All k except 1 and 2
(D) All k except 1 and 3 (E) None of these

Answer: ______



9 Which of the following, if any, is the correct guess for the particular solution yp of the differential equation
yʹʹ + y = xex + sin x ?

(A) Axex + B sin x (B) Axex + B sin x + C cos x (C) (Ax + B) ex + C sin x + D cos x
x
(D) (Ax + B) e + Cx sin x + Dx cos x (E) (Ax + B) ex + (Cx + D) sin x + (Ex + F) cos x
(F) None of these

Answer: ______