d.e. Questions

DIFFERENTIAL EQUATIONS I

1. Problem:Obtain the differential equation of the family of straight lines with slope and y intercept equal.A. y dy + ( x+1) dx = 0B. y dy – ( x+1) dx = 0C. y dx + ( x+1) dy = 0D. y dx – ( x+1) dy = 0

2. Problem:Obtain the differential equation of all straight lines with algebraic sum of the intercept fixed as k.A. (1+y’)(xy’-y)=kyB. (1-y’)(xy’+y)=kyC. (1-y’)(xy’-y)=ky D. (1+y’)(xy’+y)=ky

3. Problem:Obtain the differential equation of all straight lines at a fixed distance p from the origin.A. (xy’-y) 2=p[1+(y’)2]B. (xy’+y) 2=[1+(y’)2]C. (xy’-y) 2=p[1+(y’’)2]D. (xy’-y) =[1+y’]

4. Problem:Determine the differential equation of the family of lines passing through the origin.A. x dy – y dx = 0B. x dx – y dy = 0C. x dy + y dx = 0D. x dx + y dy = 0

5. Problem:Obtain the differential equation of all the circles with center on line y = - x and passing through the origin.

A.

B.

C.

D.

6. Problem:Obtain the differential equation of all parabolas with axis parallel to the x-axis.A. 3 ( y” )2 – y ‘ y’’’ = 0B. 3 ( y” )2 + y ‘ y’’’ = 0C. 2 ( y” )2 – y ‘ y’’’ = 0D. 2 ( y” )2 – y ‘ y’’’ = 0

7. Problem:What is the differential equation of the family of parabola’s having their vertices at the origin and their foci on the x-axis.A. 2x dx – y dy = 0B. y dx – 2x dy = 0C. 2x dx - y dy = 0D. y dx + 2x dy = 0

8. Problem:Obtain the particular solution of dr / dt = - 4rt when t = 0, r = ro

A.

B.

C.

D.

ENGINEERING MATHEMATICS H2 - 1

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9. Problem:Obtain the general solution of the differential equation xydx – (x+2)dy =0

A.

B.

C.

D.

10. Problem:Obtain the general solution of the differential equation

A.

B.

C.

D.

11. Problem:Solve the equation xy dx – (x+ 2y)2dy = 0

A.

B.

C.

D.

12. Problem:Obtain the particular solution of

; when x = 0 ‘ y

= -1.A.

B.

C.

D.

13. Problem:Solve the equation

.

A.

B.

C.

D.


.

A.

B.

C.

D.


A.

B.

C.

D.

16. Problem:Solve

A.

B.

C.

D.


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.

A.

B.

C.

D.


.

A.

B.

C.

D.

19. Problem:

Solve the equation

A.

B,

C.

D.


.

A.

B.

C.

D.

21. Problem:The differential equation

can be made exact

by using integrating factor:A. x2

B.

C. y2

D.

22. Problem:Which is not true for the differential

equation .

A. is linearB. it is homogeneousC. It is separableD. It can be solved by integrating

factor

23. Problem:A tank contains 400 liters of brine holding 100 kg of salt in solution. Water containing 125g of salt per liters flows into the tank at the rate of 12 liters per minute, and the mixture, kept uniform by stirring, flows out at the same rate. Find the amount of salt after 90 minutes.A. 53.36 kgB. 0C. 53.63 kgD. 65.33 kg

24. Problem:Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to the amount of that is unconverted at any time. If, of 75 kg at time t = 0, 8 kg is converted during the first 30 minutes, find the amount of converted in 2 hours.A. 72.73 kgB. 23.27 kgC. 27.23 kgD. 32.72 kg


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25. Problem:A thermometer reading is brought into a room where the temperature is ; 1 minute Later the thermometer reading is . Determine the thermometer reading 5 minutes after it is brought into the room.A. 62.33 o CB. 58.99 o CC. 56.55 o CD. 57.66 o C


A.

B.

C.

D.

27. Problem:The equation is the general equation ofA. y’ = 2x / yB. y’ = 2y / xC. y’ = y / 2xD. y’ = x / 2y

28. Problem:Given the following differential equations.

Solve for dy / dt.

A.

B.

C.

D.

29. Problem:The slope of a family of curves at any point ( x , y ) is equal to (x+1)(x+2). Find the equation of the curve that is passing through the point (3,3/2).

A.

B.

C.

D.

30. Problem:The slope of a family of curves at any point (x,y) is equal to Find the equation of the curve that is passing through point (1,1).

A.

B.

C.

D.


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31. Problem:The equation is the general equation of

32. Problem:Find the family of orthogonal trajectories of the system of the parabolas

A.

B.

C.

D.

33. Problem:Find the equation of the curve at every point of which, the tangent line has a slope of 2x.A. xB.

C.

D.

34. Problem:The population of a certain town increases at a rate which is numerically equal to the square root of the population present at any time. How long will it take for the population to increase from 80,000 to 150,000.A. 308.9 secs.B. 238.9 secs.C. 208.9 secs.D. 298.9 secs.

35. Problem:A nominal interest of 3% compounded continuously is given on the account. What is the accumulated amount of P10,000 after 10 years?A. P13,620.10B. P13,500.00C. P13,650.20D. P13,498.60

36. Problem:If the nominal interest rate is 3%, how much is P5,000 worth in 10 years in a continuously compounded account?A. P5,750B. P6,750C. P7,500D. P6,350

37. Problem: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 lbsB. 124.11 lbsC. 143.25 lbsD. 105.12 lbs


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38. Problem: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 3 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 kgB. 19.53 kgC. 12.62 kgD. 20.62 kg

39. Problem: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 it falls?A. 40.54B. 38.65C. 30.45D. 34.12

40. Problem:According to Newton’s law of cooling, the rate at which a substance cools in air is directly proportional to the difference between the temperature 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. 43.50 min.C. 35.39 minD. 45.30 min

41. Problem:Find the equation of the family of orthogonal trajectories of the system of parabolas y2 = 2x + C.A. y = Ce-x

B. y = Ce2x

C. y = Cex

D. y = Ce-2x

42. Problem:Radium decomposes at a rate proportional to the amount present. If half of the original amount disappears after 1000 years, what is the percentage lost in 100 years?A. 6.70%B. 4.50%C. 5.36%D. 4.30%

43. Problem: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 of inhabitants.A. 100 yearsB. 116 yearsC. 120 yearsD. 98 years

44. Problem: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. 88.60B. 95.32C. 92.16D. 90.72


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45. Problem:Determine the differential equation of the family of circles with center on the y-axis.A. (y”)3 – xy” + y’ = 0B. y” – xyy’ = 0C. xy" – (y’)3 – y’ = 0D. (y’)3 + (y")2 + xy = 0

46. Problem:Determine the differential equation of the family of lines passing through (h,k).A.

B.

C.

D.

47. Problem:What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis.A. B. C.

D.

48. Problem:Find the differential equations of the family of lines passing through the origin.A. ydx – x2 dy = 0B. xdy – ydx = 0C. xdx + ydy = 0D. ydx + xdy = 0

49. Problem:Solve the linear equation:

A.

B.

C.

D.

50. Problem:Solve

A.

B.

C.

D.

51. Problem:Solve xy’ (2y -1) = y (1 – x)A. ln (xy) = 2 ( x – y ) + CB. ln (xy) = x – 2y + CC. ln (xy) = 2y – x + CD. ln (xy) = x +2y + C

52. Problem:Find the general solution of y’ = y sec xA. 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 )

53. Problem:Find the differential equation whose general solution is y = C1x + C2ex.A. (x – 1) y” – xy’ +y = 0B. (x + 1) y” – xy’ +y = 0C. (x – 1) y” + xy’ +y = 0D. (x + 1) y” – xy’ +y = 0


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54. Problem:

Solve

A.

B.

C.

D.

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

A.

B.

C.

D. The solution is non-existing for real value of y

56. Problem:Solve the differential equation dy – xdx = 0, if the curve passes through (1,0)?A. 3x2 + 2y – 3 = 0B. 2y + x2 – 1 = 0C. x2 – 2y – 1 =0D. 2x2 + 2y - 2 =0

57. Problem:Solve (cos x cos y – cot x) dx – sin x sin y dy = 0A. 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)

58. Problem:

Find the equation of the curve at every point of which the tangent line has a slope of 2x.A. x = -y2 + CB. y = -x2 + C

C. y = x2 + CD. x = y2 + C

59. Problem:If dy = x2 dx; what is the equation of y in terms of x if the curve passes through (1,1) ?A. x2 – 3y + 3 = 0B. x3 – 3y + 2 = 0C. x3 + 3y2 + 2 = 0D. 2y +x3 + 2 = 0

60. Problem:Solve for the differential equation: x (y -1) dx + (x+1) dy = 0. If y = 2 when x = 1, determine y when x = 2.A. 1.80B. 1.48C. 1.55D. 1.63

61. Problem:The equation y2 = cx is the general solution of:

A.

B.

C.

D.

62. Problem:Which of the following equations is a variable separable DE?

A.

B.


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C.

D.

63. Problem:Which of the following equations is an exact DE?

A.

B.

C.

D.

64. Problem:Determine the order and degree of the differential equation

A. Fourth order, first degreeB. Third order, first degreeC. First order, fourth degreeD. First order, third degree


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