Differential Equations MCQs Question and Answer in Engineering Maths Page-5 section-1

41.
Solution of $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = - \frac{{\text{x}}}{{\text{y}}}$$ at x = 1 and y = √3 is

A. x - y² = -2

B. x + y² = 4

C. x² - y² = -2

D. x² + y² = 4

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42.
The solution to the ordinary differential equation $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + \frac{{{\text{dy}}}}{{{\text{dx}}}} - 6{\text{y}} = 0$$ is

A. y = c₁e^3x + c₂e^-2x

B. y = c₁e^3x + c₂e^2x

C. y = c₁e^-3x + c₂e^2x

D. y = c₁e^-3x + c₂e^-2x

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43.
Consider the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = 1 + {{\text{y}}^2}.$$
Which one of the following can be a particular solution of this differential equation?

A. y = tan(x + 3)

B. y = tan x + 3

C. x = tan(y + 3)

D. x = tan y + 3

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44.
Which ONE of the following is a linear non-homogeneous differential equation, where x and y are the independent and dependent variables respectively?

A. $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + {\text{xy}} = {{\text{e}}^{ - {\text{x}}}}$$

B. $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + {\text{xy}} = 0$$

C. $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + {\text{xy}} = {{\text{e}}^{ - {\text{y}}}}$$

D. $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + {{\text{e}}^{ - {\text{y}}}} = 0$$

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45.
A body originally at 60°C cools down to 40°C in 15 minutes when kept in air at a temperature of 25°C. What will be the temperature of the body at the end of 30 minutes?

A. 35.2°C

B. 31.5°C

C. 28.7°C

D. 15°C

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46.
The figure shows the plot of y as a function of x

The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is

A. $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} = 1$$

B. $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = {\text{x}}$$

C. $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = - {\text{x}}$$

D. $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = \left| {\text{x}} \right|$$

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47.
The following differential equation has $$3\left( {\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{t}}^2}}}} \right) + 4{\left( {\frac{{{\text{dy}}}}{{{\text{dt}}}}} \right)^3} + {{\text{y}}^{\text{2}}} + 2 = {\text{x}}$$

A. degree = 2, order = 1

B. degree = 1, order = 2

C. degree = 4, order = 3

D. degree = 2, order = 3

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48.
The boundary-value problem y'' + λy = 0, y(0) = y(π) = 0 will have non-zero solutions if and only if the values of λ are

A. 0, ±1, ±2, .....

B. 1, 2, 3, .....

C. 1, 4, 9, .....

D. 1, 9, 25, .....

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49.
The general solution of the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = \frac{{1 + \cos 2{\text{y}}}}{{1 - \cos 2{\text{x}}}}$$ is

A. tan y - cot x = c (c is a constant)

B. tan x - cot y = c (c is a constant)

C. tan y + cot x = c (c is a constant)

D. tan x + cot y = c (c is a constant)

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50.
The solution of the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + 2{\text{xy}} = {{\text{e}}^{ - {{\text{x}}^2}}}$$ with y(0) = 1 is

A. (1 + x)e^+x²

B. (1 + x)e^-x²

C. (1 - x)e^+x²

D. (1 - x)e^-x²

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Differential Equations MCQs Question and Answer in Engineering Maths

41. Solution of $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = - \frac{{\text{x}}}{{\text{y}}}$$ at x = 1 and y = √3 is

Answer & Solution

42. The solution to the ordinary differential equation $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + \frac{{{\text{dy}}}}{{{\text{dx}}}} - 6{\text{y}} = 0$$ is

Answer & Solution

43. Consider the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = 1 + {{\text{y}}^2}.$$ Which one of the following can be a particular solution of this differential equation?

Answer & Solution

44. Which ONE of the following is a linear non-homogeneous differential equation, where x and y are the independent and dependent variables respectively?

Answer & Solution

45. A body originally at 60°C cools down to 40°C in 15 minutes when kept in air at a temperature of 25°C. What will be the temperature of the body at the end of 30 minutes?

Answer & Solution

46. The figure shows the plot of y as a function of x The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is

Answer & Solution

47. The following differential equation has $$3\left( {\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{t}}^2}}}} \right) + 4{\left( {\frac{{{\text{dy}}}}{{{\text{dt}}}}} \right)^3} + {{\text{y}}^{\text{2}}} + 2 = {\text{x}}$$

Answer & Solution

48. The boundary-value problem y'' + λy = 0, y(0) = y(π) = 0 will have non-zero solutions if and only if the values of λ are

Answer & Solution

49. The general solution of the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = \frac{{1 + \cos 2{\text{y}}}}{{1 - \cos 2{\text{x}}}}$$ is

Answer & Solution

50. The solution of the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + 2{\text{xy}} = {{\text{e}}^{ - {{\text{x}}^2}}}$$ with y(0) = 1 is

Answer & Solution

41.
Solution of $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = - \frac{{\text{x}}}{{\text{y}}}$$ at x = 1 and y = √3 is

42.
The solution to the ordinary differential equation $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + \frac{{{\text{dy}}}}{{{\text{dx}}}} - 6{\text{y}} = 0$$ is

43.
Consider the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = 1 + {{\text{y}}^2}.$$
Which one of the following can be a particular solution of this differential equation?

44.
Which ONE of the following is a linear non-homogeneous differential equation, where x and y are the independent and dependent variables respectively?

45.
A body originally at 60°C cools down to 40°C in 15 minutes when kept in air at a temperature of 25°C. What will be the temperature of the body at the end of 30 minutes?

46.
The figure shows the plot of y as a function of x

The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is

47.
The following differential equation has $$3\left( {\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{t}}^2}}}} \right) + 4{\left( {\frac{{{\text{dy}}}}{{{\text{dt}}}}} \right)^3} + {{\text{y}}^{\text{2}}} + 2 = {\text{x}}$$

48.
The boundary-value problem y'' + λy = 0, y(0) = y(π) = 0 will have non-zero solutions if and only if the values of λ are

49.
The general solution of the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = \frac{{1 + \cos 2{\text{y}}}}{{1 - \cos 2{\text{x}}}}$$ is

50.
The solution of the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + 2{\text{xy}} = {{\text{e}}^{ - {{\text{x}}^2}}}$$ with y(0) = 1 is