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7. Differential Equations Problem Sets.pdf

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MULTIVECTOR REVIEW CENTER CO.
Unit M1, First Floor, CMFFI Building A, 813 Papa St. , Sampaloc, Manila
Differential Equations
EXERCISES:
1. State the order and degree of y(4) + 2(y”)2 + (y’)^4 = cos x.
A. 4, 4
C. 4, 1
B. 1, 4
D. 2, 2
2. State the order and degree of Ry” = [1 + (y’)^2]^(3/2).
A. 2, 2
C. 2, 3
B. 3, 2
D. 2, 1
3. The equation y squared = cx is the general solution of:
A. y’ = y/2x
C. y’ = 2y/x
B. y’ = x/2y
D. y’ = 2x/y
4. Eliminate the arbitrary constant of the following equation: y = C1e2x + C2e-x
A. y” – y’ – 2y = 0
C. y” – 2y + 2y = 0
B. y” – y’ + 2y = 0
D. y” – 2y’ – 2y = 0
5. Find the DE of straight lines with slope and x-intercept equal.
A. (y’)^2 = y’ – xy
C. (y’)^2 = 2xy’ – y^2
B. (y’)^2 = xy’ – y
D. (y’)^2 = 2yy’ – x^2
6. Find the general solution of 2xy dx + (x^2+ 1) dy = 0
A. x^2 + y = c
C. x^2 y + y = c
B. x^2 + 2y = c
D. x y^2 + x = c
7. Find the general solution of: [2x + y cos (xy)] dx + x cos (xy) dy = 0
A. y^2 + sin (xy) = c
C. x^2 + sin (xy) = c
B. y^2 + cos (xy) = c
D. x^2 + cos (xy) = c
8. Solve the DE: (x2 + y2) dx + 2xy dy = 0
A. x^3 + 3xy^2 = C
C. x^3 + 3x^2 y^2 = C
B. x^3 + 2xy^2 = C
D. x^3 + 2x^2 y^2 = C
9. Solve the DE: y’ = 1 + 3ytan x
A. 3y cos^3 x = c + 3 sin x – sin^3 x
C. 3y sin^3 x = c + 3 cos x – cos^3 x
B. 2y cos^2 x = c + 3 sin x – sin^2 x
D. 2y sin^3 x = c + 3 cos x – cos^2 x
3
10. Find the particular solution of y’ = x – 2xy, y(1) = 1
A. 2x = y^2 – 1 + 2 exp (1 – x^2)
C. x = y^2 – 1 + exp (1 – 2x^2)
B. 2y = x^2 – 1 + 2 exp (1 – x^2)
D. y = x^2 – 1 + exp (1 – 2x^2)
2
11. Solve y’ – 2y/x = 4xy .
A. x^2 = y(c – x^4)
C. x^2 = y^2 (c – x^4)
B. x^2 = y(c + x^4)
D. x^2 = y^2 (c + x^4)
12. The rate of population growth of a certain country is proportional to the number of inhabitants. The population is
now 50 million and 80 million 20 years later. Find the number inhabitants after 30 years.
A. 101.0 million
C. 101.2 million
B. 101.4 million
D. 101.6 million
13. Given that the half-life of a radium is 1500 years, how much in milligrams remains from one gram of radium after
2000 years?
A. 397
C. 664
B. 379
D. 646
14. According to Newton’s Law of Cooling, the rate at which a substance cools in air (medium) is directly proportional to
the difference between the temperature of the substance and that of air. If the temperature of the air is 30 deg C
and the substance cools from 100 deg C to 70 deg C in 15 minutes, how long will it take to cool 100 deg C to 50
deg C?
A. 45.30 min
C. 35.39 min
B. 43.50 min
D. 33.59 min
15. An object falls from rest in a medium offering a resistance. The velocity of the object before it reaches the ground is
given by the differential equation dv/dt + v/10 = 32. What is the velocity of the object 1 second after it falls?
A. 40.54
C. 30.45
B. 44.50
D. 34.50
This study source was downloaded by 100000863764423 from CourseHero.com on 03-12-2023 10:53:16 GMT -05:00
https://www.coursehero.com/file/85262472/7-Differential-Equations-Problem-Setspdf/
MULTIVECTOR REVIEW CENTER CO.
Unit M1, First Floor, CMFFI Building A, 813 Papa St. , Sampaloc, Manila
Differential Equations
16. A 400 gallon tank initially contains 100 gal of brine containing 50 lbs of salt. Brine containing 1lb of salt per gallon
enters the tank at the rate of 5 gal/sec, and the well-mixed brine in the tank flows out the rate of 3 gal/sec. How
much salt will be in the tank when it 300 gallons of brine?
A. 393.75 lb
C. 337.95 lb
B. 290.38 lb
D. 203.98 lb
17. In a series RL circuit, L = 4 H, R = 100 ohms and E = 200 volts, determine the current as a function of time “t”.
Assume that when the circuit is closed, there is no current in the circuit. Find the current when t = 25 ms.
A. 929 mA
C. 877 mA
B. 939 mA
D. 887 mA
2
2
18. For the family x + 3y = cy, find the member of the orthogonal trajectories which passes through (1, 2).
A. x^2 + y^2 (3x + 1) = 0
C. y^2 + x^2 (3x + 1) = 0
B. x^2 – y^2 (3x + 1) = 0
D. y^2 – x^2 (3x + 1) = 0
19. Find the particular solution of y” + 3y’ + 2y = 0 when y(0) = 0 and y’(0) = 1
A. y = exp (x) – exp (–x)
C. y = 2 exp (x) – exp (–x)
B. y = exp (–2x) – exp (–x)
D. y = exp (–x) – exp (–2x)
20. Find the general solution of y” + 7y = 0
A. y = C1 cos (7x) + C2 sin (7x)
C. y = C1 cos [sqrt(7)x] + C2 sin[sqrt(7)x]
B. y = C cos [sqrt(7)x]
D. y = C sin [sqrt(7)x]
21. Find the general solution of: y” + 6y’ + 9y = x + 1
A. y = (C1x + C2 x^2) e^(-3x) + 1/27 + x/9
C. y = (C1x + C2 x^2) e^(3x) + 1/27 + x/9
B. y = (C1 + C2 x) e^(-3x) + 1/27 + x/9
D. y = (C1 + C2 x) e^(3x) + 1/27 + x/9
22. Solve the differential equation (D^2 – D – 2)y = 12x – 6 exp (2x)
A. y = C1 e^2x + C2 e^–x – 6x + 3 + 2xe^2x
C. y = C1 e^2x + C2 e^–x + 6x + 3 + 2xe^2x
B. y = C1 e^2x + C2 e^–x – 6x + 3 – 2xe^2x
D. y = C1 e^2x + C2 e^–x + 6x – 3 – 2xe^2x
23. Solve the particular solution of (D^2 + 1)y = sec^3 x.
A. 0.5 tan x
C. 0.5 cot x
B. 0.5 sec x
D. 0.5 csc x
24. A spring is stretched 3 in by a 5 lb weight. Let the weight be pulled down 4 in below the equilibrium and then given
an upward velocity of 8 ft/sec. Find the amplitude of the motion.
A. 0.68 ft
C. 0.78 ft
B. 0.61 ft
D. 0.71 ft
25. Suppose a crossbow bolt is shot straight upward with initial velocity of 288 ft/sec. If its deceleration due to air
resistance is 0.04v, then its height x(t) satisfies the initial value problem x” = -32 – 0.04x’, x(0) = 0, x’(0) = 288. Find
the time required to reach the maximum height.
A. 7.9 sec
C. 7.0 sec
B. 7.2 sec
D. 7.7 sec
This study source was downloaded by 100000863764423 from CourseHero.com on 03-12-2023 10:53:16 GMT -05:00
https://www.coursehero.com/file/85262472/7-Differential-Equations-Problem-Setspdf/
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