Differential Equation Practice Test, Exercises of Mathematics

A series of questions related to differential equations. It covers topics such as order and degree of differential equations, variable separable DE, exact DE, particular solutions, and general solutions. The questions also involve solving equations and finding rates of decomposition. useful for students studying differential equations and can serve as study notes or exam preparation material.

Typology: Exercises

2016/2017

Available from 05/18/2022

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Differential Equation
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
2. Which of the following equations is a variable separable DE?
A. (x + x2y)dy + (2x + xy2)dx
B. (x + y)dx – 2y dy = 0
C. 2y dx = (x2 +1)dy
D. y2 dx + (2x – 3y)dy = 0
3. Obtain the particular solution of dr/dt = -4rt when t = 0, r = ro
A. r = 2ro e-2t^
2
C. r = ro e2t^
2
B. r = 2ro e-t^
2
D. r = ro e-2t^
2
4. Which of the following equations is an exact DE?
A. (X2 + 1)dx – xy dy = 0
B. x dy + (3x – 2y) dx = 0
C. 2xy dx + (2 + x2)dy = 0
D. x2y dy – y dx = 0
5. Solve the equation (6x + y2)dx + y(2x – 3y)dy = 0
A. xy2 + 3x2 – y3 = c
B. 3xy2 – 3x2 – y3 = c
C. xy2 + 2x2 – 3y3 = c
D. xy2 + 3x2 – y2 = c
6. Obtain the particular solution of (3x2 – 2y2)y’ = 2xy; when x = 0, y = -1
A. x2 = 2y2(y + 1) C. x2 = 2y2(y -1)
B. x2 = y2(y + 1) D. x2 = y2(y - 1)
7. Solve the equation dy/dx + 2/x y = 6x3
A. xy2 = 6x5 + c C. x2y2 = 6x5 + c
B. x2 = 5x6 + c D. x2y = x6 + c
8. Find the general solution of d2s/dt2 + 2 ds/dt + 5s = 0
A. s = e-t(C1cos2t + C2sin2t) C. s = e-2t(C1cos2t + C2sin2t)
B. s = 2e-t(C1cos2t + C2sin2t) D. s = 2e-2t(C1cos2t + C2sin2t)
9. Radium decomposes at a rate proportional to the amount at any instant. In
100 years, 100mg of radium decomposes to 96mg. How many mg will be left
after 100 years?
A. 88.60 C. 92.16
B. 95.32 D. 90.72
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Differential Equation

  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
  2. 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
  3. Obtain the particular solution of dr/dt = -4rt when t = 0, r = ro A. r = 2ro e-2t^^2 C. r = ro e2t^^2 B. r = 2ro e-t^^2 D. r = ro e-2t^^2
  4. 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
  5. Solve the equation (6x + y^2 )dx + y(2x – 3y)dy = 0 A. xy^2 + 3x^2 – y^3 = c B. 3xy^2 – 3x^2 – y^3 = c C. xy^2 + 2x^2 – 3y^3 = c D. xy^2 + 3x^2 – y^2 = c
  6. Obtain the particular solution of (3x^2 – 2y^2 )y’ = 2xy; when x = 0, y = - A. x^2 = 2y^2 (y + 1) C. x^2 = 2y^2 (y -1) B. x^2 = y^2 (y + 1) D. x^2 = y^2 (y - 1)
  7. Solve the equation dy/dx + 2/x y = 6x^3 A. xy^2 = 6x^5 + c C. x^2 y^2 = 6x^5 + c B. x^2 = 5x^6 + c D. x^2 y = x^6 + c
  8. Find the general solution of d^2 s/dt^2 + 2 ds/dt + 5s = 0 A. s = e-t(C 1 cos2t + C 2 sin2t) C. s = e-2t(C 1 cos2t + C 2 sin2t) B. s = 2e-t(C 1 cos2t + C 2 sin2t) D. s = 2e-2t(C 1 cos2t + C 2 sin2t)
  9. Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100mg of radium decomposes to 96mg. How many mg will be left after 100 years? A. 88.60 C. 92. B. 95.32 D. 90.
  1. 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% C. 5.36% B. 4.50% D. 4.30%
  2. The population of a country doubles in 50 years. How many years will it be five times as much? Assume the rate of increase is proportional to the number of inhabitants. A. 100 years C. 120 years B. 116 years D. 98 years
  3. If the nominal interest rate is 3%, how much is Php5,000 worth in 10 years in a continuously compounded account? A. Php5,750 C. Php7, B. Php6,750 D. Php6,
  4. A tank contains 400 liters of brine holding 100kg of salt in solution. Water containing 125kg of salt per liter flows into the tank at the rate of 12 liters per minute, and the mixture kept uniform stirring, flows out at the same rate. Find the amount of salt at the end of 90 minutes. A. 15.45 kg C. 12.62 kg B. 19.53 kg D. 20.62 kg
  5. A thermometer reading 18oC is brought into a room where temperature is 70 oC; 1 minute later the thermometer reading is 31 oC. Determine the thermometer reading 5 minutes after it is brought into the room. A. 62.33oC C. 56.55oC B. 58.99oC D. 57.66oC
  6. A 2 H inductor, 16 ohms resistor and 0.02 F capacitor is suddenly connected to a 300 volts. Find the transient current when the switch is closed at t= A. 25 e-4cos3t C. 50 e-4cos3t B. 25 e-4sin3t D. 50 e- (^4) sin3t