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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.

22Papers
15Years
38Questions
1Topics

Differential Equations question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Differential Equations. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Easy 34 89.5%
Medium 4 10.5%

Question type distribution

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

MCQ 32 84.2%
Numerical Answer Type (NAT) 5 13.2%
Fill in the blanks 1 2.6%

Subject weightage

Top subjects by unique question coverage.

Mechanical Engineering
38 Qs

Most asked topics

Top topics across the included previous year papers.

Engineering Mathematics
38 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Differential Equations
38 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) 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. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
Mechanical Engineering (ME) 202620263View paper
Mechanical Engineering (ME) 202520252View paper
Mechanical Engineering (ME) 202420241View paper
Mechanical Engineering (ME) 202320231View paper
Mechanical Engineering (ME) 2021 [Session 1]20211View paper
Mechanical Engineering (ME) 2020 [Session 2]20201View paper
Mechanical Engineering (ME) 2019 [Session 1]20191View paper
Mechanical Engineering (ME) 2019 [Session 2]20191View paper
Mechanical Engineering (ME) 2018 [Session 2]20181View paper
Mechanical Engineering (ME) 2016 [Session 1]20162View paper
Mechanical Engineering (ME) 2014 [Session 1]20142View paper
Mechanical Engineering (ME) 2014 [Session 2]20141View paper
Mechanical Engineering (ME) 2014 [Session 3]20141View paper
Mechanical Engineering (ME) 2014 [Session 4]20142View paper
Mechanical Engineering (ME) 2013 [Session 1]20133View paper
Mechanical Engineering (ME) 2013 [Session 2]20133View paper
Mechanical Engineering (ME) 2013 [Session 3]20133View paper
Mechanical Engineering (ME) 2013 [Session 4]20133View paper
Mechanical Engineering (ME) 201120111View paper
Mechanical Engineering (ME) 200920091View paper
Mechanical Engineering (ME) 200820082View paper
Mechanical Engineering (ME) 200720072View paper

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
Open complete paper
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
Open complete paper
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
Open complete paper
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
Open complete paper
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
Open complete paper
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
Open complete paper
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
Open complete paper
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 35 questions