(Last Updated On: June 8, 2023)

This is the Multiple Choice Questions Part 1 of the Series in Differential Equations topic in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

#### MCQ Topic Outline included in Mathematics Board Exam Syllabi

- MCQ in types of Differential Equations | MCQ in Order of Differential Equations | MCQs in Degree of Differential Equations | MCQ in types of solutions of Differential Equations | MCQ in Applications of Differential Equations

#### Start Practice Exam Test Questions Part 1 of the Series

**Choose the letter of the best answer in each questions.**

**Problem 1: **

Determine the order and degree of the differential equation,

A. Fourth order, first degree

B. Third order, first degree

C. First order, fourth degree

D. First order, third degree.

Answer: **Option A**

Solution: Review Solution for Number 1

**Problem 2: **

Which of the following equations is an exact DE?

A. (x^{2} + 1) dx – xy dy = 0

B. x dy + (3x – 2y) dx = 0

C. 2xy dx + (2 + x^{2}) dy = 0

D. x^{2}y dy – y dx = 0

Answer: **Option C**

Solution: Review Solution for Number 2

**Problem 3: **

Which of the following equations is a variable separable DE?

A. (x + x^{2} y) dy = (2x + xy^{2}) dx

B. (x + y) dx – 2y dy = 0

C. 2y dx = (x^{2} + 1) dy

D. y^{2} dx + (2x – 3y) dy = 0

Answer: **Option C**

Solution: Review Solution for Number 3

**Problem 4: ECE Board April 1998**

The equation y^{2} = cx is general solution of:

A. y’ = 2y / x

B. y’ = 2x / y

C. y’ = y / 2x

D. y’ = x / 2y

Answer: **Option C**

Solution: Review Solution for Number 4

**Problem 5: EE Board March 1998**

Solve the differential equation: x(y – 1) dx + (x + 1) dy = 0. If y = 2 when x = 1.

A. 1.80

B. 1.48

C. 1.55

D. 1.63

Answer: **Option C**

Solution: Review Solution for Number 5

**Problem 6: EE Board October 1997**

If dy = x^{2} dx; what is the equation of y in terms of x if the curve passes through (1, 1).

A. x^{2} – 3y + 3 = 0

B. x^{3} – 3y + 2 = 0

C. x^{3} + 3y^{2} + 2 = 0

D. 2y + x^{3} + 2 = 0

Answer: **Option B**

Solution: Review Solution for Number 6

**Problem 7: ECE Board November 1998**

Find the equation of the curve at every point of which the tangent line has a slope of 2x.

A. x = -y^{2} + C

B. y = -x^{2} + C

C. y = x^{2} + C

D. x = y^{2} + C

Answer: **Option C**

Solution: Review Solution for Number 7

**Problem 8: ECE Board April 1995**

Solve (cox x cos y – cotx) dx – sin x sin y dy = 0

A. sin x cos y = ln (c cos x)

B. sin x cos y = ln (c sin x)

C. sin x cos y = -ln (c sin x)

D. sin x cos y = -ln (c cos x)

Answer: **Option B**

Solution: Review Solution for Number 8

**Problem 9: EE Board October 1997**

Solve the differential equation dy – x dx = 0, if the curve passes through (1, 0)?

A. 3x^{2} + 2y – 3 = 0

B. 2y^{2} + x^{2} – 1 = 0

C. x^{2} – 2y – 1 = 0

D. 2x^{2} + 2y – 2 = 0

Answer: **Option C**

Solution: Review Solution for Number 9

**Problem 10: ME Board April 1996**

What is the solution of the first order differential equation y(k + 1) = y(k) + 5.

A. y(k) = 4 – 5/k

B. y(k) = 20 + 5k

C. y(k) = C – k, where C is constant

D. The solution is non-existence for real values of y.

Answer: **Option B**

Solution: Review Solution for Number 10

**Problem 11: EE Board April 1995**

Solve (y – √(x^{2} + y^{2})) dx – x dy = 0

A. √(x^{2} + y^{2} ) + y = C

B. √(x^{2} + y^{2} + y) = C

C. √(x + y) + y = C

D. √(x^{2} – y) + y = C

Answer: **Option A**

Solution: Review Solution for Number 11

**Problem 12: ECE Board November 1994**

Find the differential equation whose general solution is y = C_{1}x + C_{2}e^{x}.

A. (x – 1) y” – xy’ + y = 0

B. (x + 1) y” – xy + y = 0

C. (x – 1) y” + xy’ + y = 0

D. (x + 1) y” + xy’ + y = 0

Answer: **Option A**

Solution: Review Solution for Number 12

**Problem 13: EE Board October 1995**

Find the general solution of y’ = y sec x

A. y = C (sec x + tan x)

B. y = C (sec x – tan x)

C. y = C (sec x tan x)

D. y = C (sec2 x + tan x)

Answer: **Option A**

Solution: Review Solution for Number 13

**Problem 14: EE Board April 1996**

Solve xy’ (2y – 1) = y (1 – x)

A. ln (xy) = 2 (x – y) + C

B. ln (xy) = x – 2y + C

C. ln (xy) = 2y – x + C

D. ln (xy) = x + 2y + C

Answer: **Option D**

Solution: Review Solution for Number 14

**Problem 15: EE Board April 1996**

Solve (x + y) dy = (x – y) dx

A. x^{2} + y^{2} = C

B. x^{2} + 2xy + y^{2} = C

C. x^{2} – 2xy – y^{2} = C

D. x^{2} – 2xy + y^{2} = C

Answer: **Option C**

Solution: Review Solution for Number 15

**Problem 16: **

Solve the linear equation: dy/dx + y / x = x^{2}

A. xy2 = x^{3} / 4 + C

B. xy = x^{4} / 4 + C

C. x2y = x^{4} / 4 + C

D. y = x^{3} / 4 + C

Answer: **Option B**

Solution: Review Solution for Number 16

**Problem 17: CE Board May 1997**

Find the differential equations of the family of lines passing through the origin.

A. y dx – x dy = 0

B. x dy – y dx = 0

C. x dx + y dy = 0

D. y dx + x dy = 0

Answer: **Option B**

Solution: Review Solution for Number 17

**Problem 18: CE Board May 1996**

What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis.

A. 2x dy – y dx = 0

B. x dy + y dx = 0

C. 2y dx – x dy = 0

D. dy/dx – x = 0

Answer: **Option A**

Solution: Review Solution for Number 18

**Problem 19: CE Board November 1995**

Determine the differential equation of the family of lines passing through (h, k).

A. (y – k) dx – (x – h) dy = 0

B. (y – h) + (y – k) = dy/dx

C. (x – h) dx – (y – k) dy = 0

D. (x + h) dx – (y – k) dy = 0

Answer: **Option A**

Solution: Review Solution for Number 19

**Problem 20: **

Determine the differential equation of the family of circles with center on the y-axis.

A. (y”)3 – xy” + y’ = 0

B. y” – xyy” + y’ = 0

C. xy” – (y’)^{3} – y’ = 0

D. (y’)^{3} + (y”)^{2} + xy = 0

Answer: **Option C**

Solution: Review Solution for Number 20

**Problem 21: EE Board April 1997**

Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of radium decomposes to 96 mg. How many mg will be left after 100 years?

A. 88.60

B. 95.32

C. 92.16

D. 90.72

Answer: **Option C**

Solution: Review Solution for Number 21

**Problem 22: **

The population of a country doubles in 50 years. How many years will it be five times as much? Assume that the rate of increase is proportional to the number inhabitants.

A. 100 years

B. 116 years

C. 120 years

D. 98 years

Answer: **Option B**

Solution: Review Solution for Number 22

**Problem 23: **

Radium decomposes at a rate proportional to the amount present. If the half of the original amount disappears after 1000 years, what is the percentage lost in 100 years?

A. 6.70%

B. 4.50%

C. 5.35%

D. 4.30%

Answer: **Option A**

Solution: Review Solution for Number 23

**Problem 24: ECE Board November 1998**

Find the equation of the family of orthogonal trajectories of the system of parabolas y^{2} = 2x + C.

A. y = Ce^{-x}

B. y = Ce^{2x}

C. y = Ce^{x}

D. y = Ce^{-2x}

Answer: **Option A**

Solution: Review Solution for Number 24

**Problem 25: **

According to Newton’s law of cooling, the rate at which a substance cools in air is directly proportional to the difference between the temperatures of the substance and that of air. If the temperature of the air is 30° and the substance cools from 100° to 70° in 15 minutes, how long will it take to cool 100° to 50°?

A. 33. 59 min

B. 43.60 min

C. 35.39 min

D. 45.30 min

Answer: **Option A**

Solution: Review Solution for Number 25

**Problem 26: **

An object falls from rest in a medium offering a resistance. The velocity of the object before the object reaches the ground is given by the differential equation dV/dt + V/10 = 32, ft/sec. What is the velocity of the object one second after if falls?

A. 40.54 ft/sec

B. 38.65 ft/sec

C. 30.45 ft/sec

D. 34.12 ft/sec

Answer: **Option C**

Solution: Review Solution for Number 26

**Problem 27: **

In a tank are 100 liters of brine containing 50 kg. total of dissolved salt. Pure water is allowed to run into the tank at the rate of 3 liters a minute. Brine runs out of the tank at the rate of 2 liters a minute. The instantaneous concentration in the tank is kept uniform by stirring. How much salt is in the tank at the end of one hour?

A. 15.45 kg

B. 19.53 kg

C. 12.62 kg

D. 20.62 kg

Answer: **Option B**

Solution: Review Solution for Number 27

**Problem 28: **

A tank initially holds 100 gallons of salt solution in which 50 lbs of salt has been dissolved. A pipe fills the tank with brine at the rate of 3 gpm, containing 2 lbs of dissolved salt per gallon. Assuming that the mixture is kept uniform by stirring, a drain pipe draws out of the tank the mixture at 2 gpm. Find the amount of salt in the tank at the end of 30 minutes.

A. 171.24 lbs

B. 124.11 lbs

C. 143.25 lbs

D. 105.12 lbs

Answer: **Option A**

Solution: Review Solution for Number 28

**Problem 29: ME Board April 1998**

If the nominal interest rate is 3%, how much is P5,000 worth in 10 years in a continuous compounded account?

A. P5,750

B. P6,750

C. P7,500

D. P6,350

Answer: **Option B**

Solution: Review Solution for Number 29

**Problem 30: ME Board October 1997**

A nominal interest of 3% compounded continuously is given on the account. What is accumulated amount of P10,000 after 10 years.

A. P13,620.10

B. P13,500.10

C. P13,650.20

D. P13,498.60

Answer: **Option D**

Solution: Review Solution for Number 30

#### Online Question and Answer in Differential Equations Series

Following is the list of multiple choice questions in this brand new series:

**MCQ in Differential Equations**

**MCQ from Number 1 – 50**Answer key:

**PART 1**

**MCQ from Number 51 – 100**Answer key:

**PART 2**

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Nice questions but please answers should be added

Hello,

Do anyone have answers to the questions please

The answer could be found in the post, Just click the link

The answer could be found in the post, Just click the link

Answers

Hello! Wala po bang Part 2 MCQs ang DE?

apology, wala pa po as of now.

Kindly share answers of these mcqs…

Please, include solutions

Better

That is already given, click on the review solution option.

please check

Problem 7: ECE Board November 1998

Find the equation of the curve at every point of which the tangent line has a slope of 2x.

Please correct me if I’m wrong but I think the answer should be letter C.

I can’t check the solution for their answer since only premium members can see the solution but their answer is letter A.

yes, there was a typo error in mcq

The correct answer is C as solved in solution.

Thanks for the feedback.