Differential Equations - Engineering Mathematics - Mining Engineering Previous Year Questions

1

2007 · Mining Engineering · Engineering Mathematics · Differential Equations

Mining Engineering (MN) 2007

The solution of
ye^xdx+(4y+e^x)dy=0 for
y(0)=-1 is

A

ye^x+2y²-1=0

B

e^x+y²x-2=0

C

ye^x-y²=0

D

xe^x+y²-1=0

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2

2008 · Mining Engineering · Engineering Mathematics · Differential Equations

Mining Engineering (MN) 2008

The solution of the differential equation \[\frac{d^2y}{dx^2} + 3\frac{dy}{dx} - 4y = 0\] is

A

\(y = c_1 e^{4x}\)

B

\(y = c_1 e^{2x}\)

C

\(y = c_1 e^{x} + c_2 e^{-4x}\)

D

\(y = c_1 e^{-x} + c_2 e^{4x}\)

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3

2010 · Mining Engineering · Engineering Mathematics · Differential Equations

Mining Engineering (MN) 2010

The partial differential equation, \( r \frac{\partial \theta}{\partial r} = \text{constant} \), is a solution for

A

\(\frac{\partial^2 \theta}{\partial r^2} - \frac{1}{r} \frac{\partial \theta}{\partial r} = 0 \)

B

\(\frac{\partial^2 \theta}{\partial r^2} - \frac{\partial \theta}{\partial r} = 0 \)

C

\(r^2 \frac{\partial^2 \theta}{\partial r^2} + r \frac{\partial \theta}{\partial r} = 0 \)

D

\(\frac{\partial^2 \theta}{\partial r^2} + \frac{1}{r} \frac{\partial \theta}{\partial r} = 0 \)

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4

2012 · Mining Engineering · Engineering Mathematics · Differential Equations

Mining Engineering (MN) 2012

The 2^nd order differential equation having a solution y = (A / x) + B, where A and B are constants, is

A

\(\frac{d^2y}{dydx} + \frac{2}{x}\frac{dy}{dx} = 0\)

B

\(\frac{d^2y}{dx^2} + \frac{2}{x}\frac{dy}{dx} = 0\)

C

\((\frac{d^2y}{dx^2})^2 + \frac{2}{x}\frac{dy}{dx} = 0\)

D

\(\frac{d^2y}{dydx} + \frac{d^2y}{dx^2} + \frac{dy}{dx} = 0\)

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5

2013 · Mining Engineering · Engineering Mathematics · Differential Equations

Mining Engineering (MN) 2013

Given the following differential equation
\(\frac{d^2 y}{dx^2} + 7 \frac{dy}{dx} + 12y = 0\)
the general solution is

A

\(y = Ae^{4x} + Be^{-3x}\)

B

\(y = Ae^{-4x} + Be^{-3x}\)

C

\(y = Ae^{3x} + Be^{-4x}\)

D

\(y = Ae^{4x} + Be^{3x}\)

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6

2014 · Mining Engineering · Engineering Mathematics · Differential Equations

Mining Engineering (MN) 2014

Solution of the differential equation dy/dx = ky follows exponential decay (where k is a constant) for x ∈ [0, ∞] if

A

k > 0

B

k < 0

C

k = 0

D

k = e

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7

2018 · Mining Engineering · Engineering Mathematics · Differential Equations

Mining Engineering (MN) 2018

The degree of the differential equation \(\frac{d^2x}{dr^2}+2x^3=0\) is ______________.

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8

2018 · Mining Engineering · Engineering Mathematics · Differential Equations

Mining Engineering (MN) 2018

If \( c \) is a constant, the solution of the differential equation \( 4y\frac{dy}{dx} + 9x = 0 \) is

A

\(\frac{x^2}{81} + \frac{y^2}{16} = c \)

B

\(\frac{x^2}{16} + \frac{y^2}{81} = c \)

C

\(\frac{x^2}{9} + \frac{y^2}{4} = c \)

D

\(\frac{x^2}{4} + \frac{y^2}{9} = c \)

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9

2020 · Mining Engineering · Engineering Mathematics · Differential Equations

Mining Engineering (MN) 2020

For the differential equation \( y\sqrt{1-x^2} \, dy + x\sqrt{1-y^2} \, dx = 0 \), assuming the constant of integration to be \( C \), the general solution is

A

\(\frac{1}{\sqrt{1-x^2}} + \frac{1}{\sqrt{1-y^2}} = C \)

B

\(y\sqrt{1-x^2} + x\sqrt{1-y^2} = C \)

C

\(\sqrt{1-x} + \sqrt{1-y} = C \)

D

\(\sqrt{1-x^2} + \sqrt{1-y^2} = C \)

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10

2021 · Mining Engineering · Engineering Mathematics · Differential Equations

Mining Engineering (MN) 2021

Assume that COVID-19 growth rate of number of infections per day (c) in a certain population is represented by the following differential equation.
\(100\frac{dc}{dt} - 7c = 0\)
Where, t stands for time in days. Time taken for the number of infections per day to double, in days, is _______. [round off to the nearest integer]

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11

2022 · Mining Engineering · Engineering Mathematics · Differential Equations

Mining Engineering (MN) 2022

Let \( \frac{dT}{dt} \propto (T_R - T) \), where \( T_R \) and \( T \) are temperatures in degree centigrade of a room and thermometer, respectively, and \( t \) denotes time in minutes. A thermometer at a reading of \( 2^\circ C \) is brought in a room of temperature \( 40^\circ C \). Two minutes later, the thermometer reads \( 15^\circ C \). The time elapsed in minutes when the thermometer reads \( 39.5^\circ C \), is __________. (round off to two decimal places)

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