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Previous year question hub

Existence, Uniqueness and Linear Equations - Ordinary Differential Equations - Mathematics Previous Year Questions

Practice Existence, Uniqueness and Linear Equations - Ordinary Differential Equations - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

20Papers
20Years
66Questions
1Topics

Existence, Uniqueness and Linear 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.

Medium 51 77.3%
Easy 13 19.7%
Hard 2 3%

Question type distribution

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

MCQ 48 72.7%
Numerical Answer Type (NAT) 16 24.2%
MSQ 2 3%

Subject weightage

Top subjects by unique question coverage.

Mathematics
66 Qs

Most asked topics

Top topics across the included previous year papers.

Ordinary Differential Equations
66 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Existence, Uniqueness and Linear Equations
66 Qs

Paper coverage

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

Mathematics (MA) 2026
3 Qs
Mathematics (MA) 2025
3 Qs
Mathematics (MA) 2024
3 Qs
Mathematics (MA) 2023
2 Qs
Mathematics (MA) 2022
2 Qs
Mathematics (MA) 2021
1 Qs
Mathematics (MA) 2020
4 Qs
Mathematics (MA) 2019
2 Qs
Mathematics (MA) 2018
5 Qs
Mathematics (MA) 2017
5 Qs
Mathematics (MA) 2016
6 Qs
Mathematics (MA) 2015
1 Qs
Mathematics (MA) 2014
2 Qs
Mathematics (MA) 2013
3 Qs
Mathematics (MA) 2012
4 Qs
Mathematics (MA) 2011
1 Qs
Mathematics (MA) 2010
3 Qs
Mathematics (MA) 2009
5 Qs
Mathematics (MA) 2008
5 Qs
Mathematics (MA) 2007
6 Qs

Included previous year papers

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

Paper nameYearPDFAttempt
Mathematics (MA) 20262026
3 questions in this view		2026
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Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mathematics (MA) 20252025
3 questions in this view		2025
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mathematics (MA) 20242024
3 questions in this view		2024
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mathematics (MA) 20232023
2 questions in this view		2023
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Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mathematics (MA) 20222022
2 questions in this view		2022
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ExamElite solutions
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Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mathematics (MA) 20212021
1 questions in this view		2021
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ExamElite solutions
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Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mathematics (MA) 20202020
4 questions in this view		2020
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20192019
2 questions in this view		2019
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20182018
5 questions in this view		2018
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20172017
5 questions in this view		2017
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20162016
6 questions in this view		2016
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20152015
1 questions in this view		2015
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20142014
2 questions in this view		2014
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ExamElite solutions
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Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20132013
3 questions in this view		2013
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20122012
4 questions in this view		2012
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20112011
1 questions in this view		2011
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20102010
3 questions in this view		2010
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20092009
5 questions in this view		2009
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20082008
5 questions in this view		2008
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Mathematics (MA) 20072007
6 questions in this view		2007
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download

All Existence, Uniqueness and Linear Equations previous year questions

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

1
2008 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2008
Let \(y\) be a solution of \(y' = e^{-y^2} - 1\) on \([0, 1]\) which satisfies \(y(0) = 0\). Then
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2
2008 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2008
For the equation \(x(x-1)y'' + \sin(x)y' + 2x(x-1)y = 0\), consider the following statements P: \(x = 0\) is a regular singular point. Q: \(x = 1\) is a regular singular point. Then
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3
2008 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2008
Let \(y_1\) and \(y_2\) be two linearly independent solutions of \(y'' + (\sin x) y = 0, 0 \le x \le 1\). Let \(g(x) = W(y_1, y_2)(x)\) be the Wronskian of \(y_1\) and \(y_2\). Then
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4
2008 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2008
One particular solution of \(y''' - y'' - y' + y = -e^x\) is a constant multiple of
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5
2008 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2008
Let \(n \geq 3\) be an integer. Let \(y\) be the polynomial solution of \((1 - x^2) y'' - 2xy' + n(n - 1)y = 0\) satisfying \(y(1) = 1\). Then the degree of \(y\) is
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6
2009 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2009
The resolvent kernel for the integral equation u(x) = F(x) + ∫0x et–x u(t) dt is
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7
2009 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2009
If \(D \equiv \frac{d}{dx}\) then the value of \(\frac{1}{(xD+1)} (x^{-1})\) is
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8
2009 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2009
The equation \((\alpha xy^3 + y \cos x) dx + (x^3 y^2 + \beta \sin x) dy = 0\) is exact for
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9
2009 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2009
If \( y(x) = x \) is a solution of the differential equation \( y'' - \left( \frac{2}{x^2} + \frac{1}{x} \right) (xy' - y) = 0, \ 0 < x < \infty \), then its general solution is
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10
2009 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2009
The set of initial conditions for which the above differential equation has NO solution is
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11
2010 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2010
The maximum number of linearly independent solutions of the differential equation \( \frac{d^4 y}{dx^4} = 0 \), with the condition \( y(0) = 1 \), is
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12
2010 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2010
Let \( y(x) \) be the solution of the initial value problem
\( y'' - y' + 4y' - 4y = 0, \quad y(0) = y'(0) = 2, y''(0) = 0. \)
Then the value of \( y(\frac{\pi}{2}) \) is
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13
2010 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2010
Let \( y(x) \) be the solution of the initial value problem
\( x^2 y'' + xy' + y = x, \quad y(1) = y'(1) = 1. \)
Then the value of \( y(e^{\frac{\pi}{2}}) \) is
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14
2011 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2011
The initial value problem \( x \frac{dy}{dx} = y + x^2, x > 0; y(0) = 0, \) has
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15
2012 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2012
If a transformation \(y=uv\) transforms the given differential equation \(f(x)y''-4f'(x)y'+g(x)y=0\) into the equation of the form \(v''+h(x)v=0\), then \(u\) must be
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16
2012 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2012
If \(y=\sum_{m=0}^{\infty} c_m x^{r+m}\) is assumed to be a solution of the differential equation \(x^2y''-xy'-3(1+x^2)y=0\), then the values of \(r\) are
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17
2012 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2012
Let \( f(x) \) and \( xf(x) \) be the particular solutions of a differential equation
\( y'' + R(x)y' + S(x)y = 0 \).
Then the solution of the differential equation \( y'' + R(x)y' + S(x)y = f(x) \) is
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18
2012 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2012
Choose the most appropriate alternative from the options given below to complete the following sentence:
If the tired soldier wanted to lie down, he ___ the mattress out on the balcony.
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19
2013 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2013
Assume that all the zeros of the polynomial \(a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0\) have negative real parts. If \(u(t)\) is any solution to the ordinary differential equation \(a_n \frac{d^n u}{dt^n} + a_{n-1} \frac{d^{n-1} u}{dt^{n-1}} + \cdots + a_1 \frac{du}{dt} + a_0 u = 0\), then \(\lim_{t \to \infty} u(t)\) is equal to
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20
2013 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2013
The product \(W(y_1, y_2) P(x)\) equals
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Showing 20 of 65 questions