Differential Equations - Engineering Mathematics - Electrical Engineering Previous Year Questions

1

2007 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2007

The differential equation \(\frac{dx}{dt} = \frac{1-x}{\tau}\) is discretised using Euler's numerical integration method with a time step \(\Delta T > 0\). What is the maximum permissible value of \(\Delta T\) to ensure stability of the solution of the corresponding discrete time equation?

A

1

B

\(\tau / 2\)

C

\(\tau\)

D

\(2\tau\)

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2

2010 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2010

For the differential equation \frac{d^2x}{dt^2}+6\frac{dx}{dt}+8x=0 with initial conditions x(0)=1 and \frac{dx}{dt}\big|_{t=0}=0, the solution is

A

x(t) = 2e^{-6t} - e^{-2t}

B

x(t) = 2e^{-2t} - e^{-4t}

C

x(t) = -e^{-6t} + 2e^{-4t}

D

x(t) = e^{-2t} + 2e^{-4t}

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3

2011 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2011

With \(K\) as a constant, the possible solution for the first order differential equation \(\frac{dy}{dx}=e^{-3x}\) is

A

\(-\frac{1}{3}e^{-3x}+K\)

B

\(-\frac{1}{3}e^{3x}+K\)

C

\(-3e^{-3x}+K\)

D

\(-3e^{-3x}+K\)

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4

2012 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2012

With initial condition \(x(1) = 0.5\), the solution of the differential equation \(t\frac{dx}{dt} + x = t\) is

A

\(x = t - \frac{1}{2}\)

B

\(x = t^2 - \frac{1}{2}\)

C

\(x = \frac{t^2}{2}\)

D

\(x = \frac{t}{2}\)

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5

2014 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2014 [Session 1]

The solution for the differential equation \[ \frac{d^2 x}{dt^2} = -9 x \] with initial conditions \( x(0) = 1 \) and \( \frac{dx}{dt} \big|_{t=0} = 1 \), is

A

\(t^2 + t + 1 \)

B

\(\sin 3t + \frac{1}{3} \cos 3t + \frac{2}{3} \)

C

\(\frac{1}{3} \sin 3t + \cos 3t \)

D

\(\cos 3t + t \)

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6

2014 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2014 [Session 2]

Consider the differential equation \( x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} - y = 0 \). Which of the following is a solution to this differential equation for \( x > 0 \)?

A

\(e^x \)

B

\(x^2 \)

C

\(1/x \)

D

\(\ln x \)

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7

2016 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2016 [Session 1]

A function \(y(t)\), such that \(y(0) = 1\) and \(y(1) = 3e^{-1}\), is a solution of the differential equation \(\frac{d^2y}{dt^2} + 2\frac{dy}{dt} + y = 0\). Then \(y(2)\) is

A

\(5e^{-1}\)

B

\(5e^{-2}\)

C

\(7e^{-1}\)

D

\(7e^{-2}\)

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8

2016 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2016 [Session 2]

Let \(y(x)\) be the solution of the differential equation \(\frac{d^2 y}{dx^2} - 4\frac{dy}{dx} + 4y = 0\) with initial conditions \(y(0) = 0\) and \(\left.\frac{dy}{dx}\right|_{x=0} = 1\). Then the value of \(y(1)\) is ______.

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9

2017 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2017 [Session 1]

Consider the differential equation $(t^2-81)\frac{dy}{dt} + 5t y = \sin(t)$ with $y(1)=2\pi$. There exists a unique solution for this differential equation when $t$ belongs to the interval

A

$(-2,2)$

B

$(-10,10)$

C

$(-10,2)$

D

$(0,10)$

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10

2020 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2020

Consider the initial value problem below. The value of \(y\) at \(x = \ln 2\), (rounded off to 3 decimal places) is __________. \[\frac{dy}{dx} = 2x - y, \quad y(0) = 1\]

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11

2023 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2023

In the following differential equation, the numerically obtained value of \(y(t)\), at \(t = 1\), is __________ (Round off to 2 decimal places).
\[\frac{dy}{dt} = \frac{e^{-\alpha t}}{2 + \alpha t}, \quad \alpha = 0.01 \text{ and } y(0) = 0\]

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12

2024 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2024

Which of the following differential equations is/are nonlinear?

A

t x(t) + \frac{dx(t)}{dt} = t^2 e^t, \quad x(0) = 0

B

\(\frac{1}{2} e^t + x(t) \frac{dx(t)}{dt} = 0, \quad x(0) = 0\)

C

x(t) \cos t - \frac{dx(t)}{dt} \sin t = 1, \quad x(0) = 0

D

x(t) + e^{\left(\frac{dx(t)}{dt}\right)} = 1, \quad x(0) = 0

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13

2026 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2026

Consider the following differential equation:
\[ t^2 \frac{d^2y}{dt^2} + 7t \frac{dy}{dt} + 8ty = 10 \sin(t) \]
Which one of the following options is correct?

A

It is a linear differential equation

B

It is a nonlinear differential equation

C

It is a time-invariant differential equation

D

It is a second-order partial differential equation

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14

2026 · Electrical Engineering · Engineering Mathematics · Differential Equations

Electrical Engineering (EE) 2026

Consider the second-order differential equation \[\frac{d^2y}{dx^2}+\frac{dy}{dx}+y=0\] with initial conditions \[y(0)=1, \quad \left.\frac{dy}{dx}\right|_{x=0}=1\] The solution is given by

A

\(y(x)=\exp(-x/2)\left(\cos\left(\frac{\sqrt{3}x}{2}\right)+\sqrt{3}\sin\left(\frac{\sqrt{3}x}{2}\right)\right)\)

B

\(y(x)=\exp(-x/2)\left(\cos\left(\frac{\sqrt{3}x}{2}\right)+\frac{1}{\sqrt{3}}\sin\left(\frac{\sqrt{3}x}{2}\right)\right)\)

C

\(y(x)=\exp(-x/2)\left(\cos\left(\frac{\sqrt{3}x}{2}\right)-\frac{1}{\sqrt{3}}\sin\left(\frac{\sqrt{3}x}{2}\right)\right)\)

D

\(y(x)=\exp(-x/2)\left(\cos\left(\frac{\sqrt{3}x}{2}\right)-\sqrt{3}\sin\left(\frac{\sqrt{3}x}{2}\right)\right)\)

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