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

A) x - y² = -2 B) x + y² = 4 C) x² - y² = -2 D) x² + y² = 4

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Answer & Solution

Answer: Option D

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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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Answer & Solution

Answer: Option C

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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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Answer & Solution

Answer: Option A

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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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Answer & Solution

Answer: Option A

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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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Answer & Solution

Answer: Option B

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46

The figure shows the plot of y as a function of x
Differential Equations mcq question image

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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Answer & Solution

Answer: Option D

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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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Answer & Solution

Answer: Option B

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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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Answer & Solution

Answer: Option C

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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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Answer & Solution

Answer: Option C

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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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Answer & Solution

Answer: Option B

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