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Previous year question hub

Differential Equations - Engineering Mathematics - Mechanical Engineering Previous Year Questions

Practice Differential Equations - Engineering Mathematics - Mechanical Engineering previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

23Papers
16Years
39Questions
1Topics

Differential Equations question pattern

Every graph below is calculated only from this selection.

Questions by year

Compare question counts across years.

Difficulty distribution

How the classified questions are distributed by difficulty.

Easy 35 89.7%
Medium 4 10.3%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

MCQ 32 82.1%
Numerical Answer Type (NAT) 6 15.4%
Fill in the blanks 1 2.6%

Subject weightage

Top subjects by unique question coverage.

Mechanical Engineering
39 Qs

Most asked topics

Top topics across the included previous year papers.

Engineering Mathematics
39 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Differential Equations
39 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

Mechanical Engineering (ME) 2026
3 Qs
Mechanical Engineering (ME) 2025
2 Qs
Mechanical Engineering (ME) 2024
1 Qs
Mechanical Engineering (ME) 2023
1 Qs
Mechanical Engineering (ME) 2021 [Session 1]
1 Qs
Mechanical Engineering (ME) 2020 [Session 2]
1 Qs
Mechanical Engineering (ME) 2019 [Session 1]
1 Qs
Mechanical Engineering (ME) 2019 [Session 2]
1 Qs
Mechanical Engineering (ME) 2018 [Session 2]
1 Qs
Mechanical Engineering (ME) 2017 [Session 2]
1 Qs
Mechanical Engineering (ME) 2016 [Session 1]
2 Qs
Mechanical Engineering (ME) 2014 [Session 1]
2 Qs
Mechanical Engineering (ME) 2014 [Session 4]
2 Qs
Mechanical Engineering (ME) 2014 [Session 2]
1 Qs
Mechanical Engineering (ME) 2014 [Session 3]
1 Qs
Mechanical Engineering (ME) 2013 [Session 1]
3 Qs
Mechanical Engineering (ME) 2013 [Session 2]
3 Qs
Mechanical Engineering (ME) 2013 [Session 3]
3 Qs
Mechanical Engineering (ME) 2013 [Session 4]
3 Qs
Mechanical Engineering (ME) 2011
1 Qs
Mechanical Engineering (ME) 2009
1 Qs
Mechanical Engineering (ME) 2008
2 Qs
Mechanical Engineering (ME) 2007
2 Qs

Included previous year papers

Newest papers appear first. Search these papers or sort by year and name.

Paper nameYearPDFAttempt
Mechanical Engineering (ME) 20262026
3 questions in this view		2026
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 20252025
2 questions in this view		2025
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 20242024
1 questions in this view		2024
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 20232023
1 questions in this view		2023
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2021 [Session 1]2021
1 questions in this view		2021
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2020 [Session 2]2020
1 questions in this view		2020
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2019 [Session 1]2019
1 questions in this view		2019
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2019 [Session 2]2019
1 questions in this view		2019
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2018 [Session 2]2018
1 questions in this view		2018
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2017 [Session 2]2017
1 questions in this view		2017
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2016 [Session 1]2016
2 questions in this view		2016
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2014 [Session 1]2014
2 questions in this view		2014
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2014 [Session 2]2014
1 questions in this view		2014
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2014 [Session 3]2014
1 questions in this view		2014
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2014 [Session 4]2014
2 questions in this view		2014
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2013 [Session 1]2013
3 questions in this view		2013
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2013 [Session 2]2013
3 questions in this view		2013
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2013 [Session 3]2013
3 questions in this view		2013
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2013 [Session 4]2013
3 questions in this view		2013
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 20112011
1 questions in this view		2011
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 20092009
1 questions in this view		2009
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 20082008
2 questions in this view		2008
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 20072007
2 questions in this view		2007
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download

All Differential Equations previous year questions

Practice every matching question in batches of 20, with every available option.

1
2007 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2007
The partial differential equation \( \frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2} + \left( \frac{\partial \phi}{\partial x} \right) + \left( \frac{\partial \phi}{\partial y} \right) = 0 \) has
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2
2007 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2007
The solution of \( \frac{dy}{dx} = y^2 \) with initial value \( y(0) = 1 \) is bounded in the interval
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3
2008 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2008
Given that \(\ddot{x} + 3x = 0\), and \(x(0) = 1\), \(\dot{x}(0) = 0\), what is \(x(1)\)?
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4
2008 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2008
It is given that \(y'' + 2y' + y = 0, y(0) = 0, y(1) = 0\). What is \(y(0.5)\)?
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5
2009 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2009
The solution of \( x \frac{dy}{dx} + y = x^4 \) with the condition \( y(1) = \frac{6}{5} \) is
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6
2011 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2011
Consider the differential equation \( \frac{dy}{dx} = (1 + y^2)x \). The general solution with constant \( c \) is
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7
2013 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2013 [Session 1]
The partial differential equation \(\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} = \frac{\partial^2 u}{\partial x^2}\) is a
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8
2013 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2013 [Session 1]
The function \( f(t) \) satisfies the differential equation \( \frac{d^2 f}{dt^2} + f = 0 \) and the auxiliary conditions, \( f(0) = 0 \), \( \frac{df}{dt}(0) = 4 \). The Laplace transform of \( f(t) \) is given by
Open complete paper
9
2013 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2013 [Session 1]
The solution to the differential equation d²u/dx² - k du/dx = 0 where k is a constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is
Open complete paper
10
2013 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2013 [Session 2]
The partial differential equation \(\frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} = \frac{\partial^2 u}{\partial x^2}\) is a
Open complete paper
11
2013 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2013 [Session 2]
The solution to the differential equation \(\frac{d^2u}{dx^2} - k\frac{du}{dx} = 0\) where \(k\) is a constant, subjected to the boundary conditions \(u(0) = 0\) and \(u(L) = U\), is
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12
2013 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2013 [Session 3]
The partial differential equation ∂u/∂t + u ∂u/∂x = ∂²u/∂x² is a
Open complete paper
13
2013 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2013 [Session 3]
The function f(t) satisfies the differential equation \(\frac{d^2 f}{dt^2} + f = 0\) and the auxiliary conditions, f(0) = 0, \(\frac{df}{dt}(0) = 4\). The Laplace transform of f(t) is given by
Open complete paper
14
2013 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2013 [Session 3]
The solution to the differential equation \(\frac{d^2 u}{dx^2} - k\frac{du}{dx} = 0\) where k is a constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is
Open complete paper
15
2013 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2013 [Session 4]
The function \(f(t)\) satisfies the differential equation \(\frac{d^2f}{dt^2} + f = 0\) and the auxiliary conditions, \(f(0) = 0\), \(\frac{df}{dt}(0) = 4\). The Laplace transform of \(f(t)\) is given by
Open complete paper
16
2014 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2014 [Session 1]
The matrix form of the linear system \[ \frac{dx}{dt} = 3x - 5y \] and \[ \frac{dy}{dt} = 4x + 8y \] is
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17
2014 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2014 [Session 1]
If y = f(x) is the solution of \(\frac{d^2 y}{dx^2} = 0\) with the boundary conditions y = 5 at x = 0, and \(\frac{dy}{dx} = 2\) at x = 10, f(15) = ______
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18
2014 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2014 [Session 2]
The general solution of the differential equation \(\frac{dy}{dx} = \cos(x+y)\), with \(c\) as a constant, is
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19
2014 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2014 [Session 3]
Consider two solutions \(x(t) = x_1(t)\) and \(x(t) = x_2(t)\) of the differential equation \(\frac{d^2x(t)}{dt^2} + x(t) = 0, t > 0\), such that \(x_1(0) = 1, \frac{dx_1(t)}{dt}\big|_{t=0} = 0\), \(x_2(0) = 0, \frac{dx_2(t)}{dt}\big|_{t=0} = 1\). The Wronskian \(W(t) = \begin{vmatrix} x_1(t) & x_2(t) \\ \frac{dx_1(t)}{dt} & \frac{dx_2(t)}{dt} \end{vmatrix}\) at \(t = \pi/2\) is
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20
2014 · Mechanical Engineering · Engineering Mathematics · Differential Equations
Mechanical Engineering (ME) 2014 [Session 4]
The solution of the initial value problem \(\frac{dy}{dx} = -2xy; \quad y(0) = 2\) is
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Showing 20 of 36 questions