My Cart
Your Cart 0

    Your cart is empty.

  • Total (Amount) ₹0.00
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
63Questions
1Topics

Existence, Uniqueness and Linear Equations question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Existence, Uniqueness and Linear Equations. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 49 77.8%
Easy 12 19%
Hard 2 3.2%

Question type distribution

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

MCQ 43 68.3%
Numerical Answer Type (NAT) 16 25.4%
MSQ 4 6.3%

Subject weightage

Top subjects by unique question coverage.

Mathematics
63 Qs

Most asked topics

Top topics across the included previous year papers.

Ordinary Differential Equations
63 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Existence, Uniqueness and Linear Equations
63 Qs

Paper coverage

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

Mathematics (MA) 2026
2 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
3 Qs
Mathematics (MA) 2011
1 Qs
Mathematics (MA) 2010
4 Qs
Mathematics (MA) 2009
5 Qs
Mathematics (MA) 2008
5 Qs
Mathematics (MA) 2007
4 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
Mathematics (MA) 202620262View paper
Mathematics (MA) 202520253View paper
Mathematics (MA) 202420243View paper
Mathematics (MA) 202320232View paper
Mathematics (MA) 202220222View paper
Mathematics (MA) 202120211View paper
Mathematics (MA) 202020204View paper
Mathematics (MA) 201920192View paper
Mathematics (MA) 201820185View paper
Mathematics (MA) 201720175View paper
Mathematics (MA) 201620166View paper
Mathematics (MA) 201520151View paper
Mathematics (MA) 201420142View paper
Mathematics (MA) 201320133View paper
Mathematics (MA) 201220123View paper
Mathematics (MA) 201120111View paper
Mathematics (MA) 201020104View paper
Mathematics (MA) 200920095View paper
Mathematics (MA) 200820085View paper
Mathematics (MA) 200720074View paper

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
Open complete paper
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
Open complete paper
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
Open complete paper
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
Open complete paper
5
2008 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2008
The integral equation \(x(t) - \int_{0}^{1} [\cos t \sec s \cdot x(s)] ds = \sinh t, 0 \leq t \leq 1\), has
Open complete paper
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
Open complete paper
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
Open complete paper
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
Open complete paper
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
Open complete paper
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
Open complete paper
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
Open complete paper
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
Open complete paper
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
Open complete paper
14
2010 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2010
For a continuous function \( f(t) \), \( 0 \le t \le 1 \), the integral equation \( y(t) = f(t) + 3 \int_0^1 t s y(s) ds \) has
Open complete paper
15
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
Open complete paper
16
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
Open complete paper
17
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
Open complete paper
18
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
Open complete paper
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
Open complete paper
20
2013 · Mathematics · Ordinary Differential Equations · Existence, Uniqueness and Linear Equations
Mathematics (MA) 2013
The product \(W(y_1, y_2) P(x)\) equals
Open complete paper

Showing 20 of 62 questions