ExamSIDE
Questions
ExamSIDE.Com
Mathematics
Trigonometry
Trigonometric Functions & Equations
Properties of Triangle
Inverse Trigonometric Functions
Algebra
Logarithms
Sequence and Series
Quadratic Equations
Complex Numbers
Permutations and Combinations
Mathematical Induction and Binomial Theorem
Matrices and Determinants
Vector Algebra
Three Dimensional Geometry
Probability
Statistics
Sets and Relations
Calculus
Functions
Definite Integration
Application of Integration
Limits, Continuity and Differentiability
Differentiation
Application of Derivatives
Indefinite Integrals
Differential Equations
Coordinate Geometry
Straight Lines and Pair of Straight Lines
Circle
Parabola
Ellipse and Hyperbola
Joint Entrance Examination
JEE Main
Chemistry
Physics
Mathematics
JEE Advanced
Physics
Chemistry
Mathematics
WB JEE
Physics
Chemistry
Mathematics
Graduate Aptitude Test in Engineering
GATE CSE
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
GATE ECE
Network Theory
Control Systems
Electronic Devices and VLSI
Analog Circuits
Digital Circuits
Microprocessors
Signals and Systems
Communications
Electromagnetics
General Aptitude
Engineering Mathematics
GATE EE
Electromagnetic Fields
Signals and Systems
Engineering Mathematics
General Aptitude
Power Electronics
Power System Analysis
Analog Electronics
Control Systems
Digital Electronics
Electrical Machines
Electric Circuits
Electrical and Electronics Measurement
GATE ME
Engineering Mechanics
Strength of Materials
Theory of Machines
Engineering Mathematics
Machine Design
Fluid Mechanics
Turbo Machinery
Heat Transfer
Thermodynamics
Production Engineering
Industrial Engineering
General Aptitude
GATE CE
Engineering Mechanics
Strength of Materials Or Solid Mechanics
Structural Analysis
Construction Material and Management
Reinforced Cement Concrete
Steel Structures
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Hydrology
Irrigation
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
Engineering Mathematics
General Aptitude
GATE PI
Fluid Mechanics
Metrology
Theory of Machines
Engineering Mathematics
Heat Transfer
Machine Tools and Machining
Industrial Engineering
Engineering Mechanics
Strength of Materials
Thermodynamics
Machine Design
Casting
Joining of Materials
Metal Forming
GATE IN
Engineering Mathematics
Medical
NEET
Biology
Chemistry
Physics
NEW
New Website Launch
Experience the best way to solve previous year questions with
mock tests
(very detailed analysis),
bookmark your favourite questions
,
practice
etc...
VISIT NOW
WB JEE
Differential Equations
Mathematics
Previous Years Questions
START HERE
MCQ (Single Correct Answer)
More
If the transformation $$z = \log \tan {x \over 2}$$ reduces the differential equation $${{{d^2}y} \over {d{x^2}}} + \cot...
WB JEE 2022
GO TO QUESTION
The solution of $$\cos y{{dy} \over {dx}} = {e^{x + \sin y}} + {x^2}{e^{\sin y}}$$ is $$f(x) + {e^{ - \sin y}} = C$$ (C ...
WB JEE 2022
GO TO QUESTION
The differential of $$f(x) = {\log _e}(1 + {e^{10x}}) - {\tan ^{ - 1}}({e^{5x}})$$ at x = 0 and for dx = 0.2 is
WB JEE 2021
GO TO QUESTION
If $$x{{dy} \over {dx}} + y = {{xf(xy)} \over {f'(xy)'}}$$, then | f(xy) | is equal to (where k is an arbitrary positive...
WB JEE 2021
GO TO QUESTION
The differential equation of all the ellipses centred at the origin and have axes as the co-ordinate axes is where $$y^{...
WB JEE 2021
GO TO QUESTION
Let $$y = {1 \over {1 + x + lnx}}$$, then
WB JEE 2020
GO TO QUESTION
Let $$y = f(x) = 2{x^2} - 3x + 2$$. The differential of y when x changes from 2 to 1.99 is
WB JEE 2020
GO TO QUESTION
The differential equation of the family of curves y = ex (A cos x + B sin x) where, A, B are arbitrary constants is...
WB JEE 2020
GO TO QUESTION
If $$x\sin \left( {{y \over x}} \right)dy = \left[ {y\sin \left( {{y \over x}} \right) - x} \right]dx,\,x > 0$$ and $...
WB JEE 2020
GO TO QUESTION
Let f be a differentiable function with $$\mathop {\lim }\limits_{x \to \infty } f(x) = 0.$$ If $$y' + yf'(x) - f(x)f'(x...
WB JEE 2020
GO TO QUESTION
Let cos$$^{ - 1}\left( {{y \over b}} \right) = \log {\left( {{x \over n}} \right)^n}$$. Then
WB JEE 2020
GO TO QUESTION
General solution of $${(x + y)^2}{{dy} \over {dx}} = {a^2},a \ne 0$$ is (C is an arbitrary constant)
WB JEE 2019
GO TO QUESTION
The general solution of the differential equation $$\left( {1 + {e^{{x \over y}}}} \right)dx + \left( {1 - {x \over y}} ...
WB JEE 2019
GO TO QUESTION
Let y(x) be a solution of $$(1 + {x^2}){{dy} \over {dx}} + 2xy - 4{x^2} = 0$$. Then y(1) is equal to
WB JEE 2018
GO TO QUESTION
The differential equation representing the family of curves $${y^2} = 2d(x + \sqrt d )$$, where d is a parameter, is of
WB JEE 2018
GO TO QUESTION
The integrating factor of the first order differential equation $${x^2}({x^2} - 1){{dy} \over {dx}} + x({x^2} + 1)y = {x...
WB JEE 2017
GO TO QUESTION
Solution of $${(x + y)^2}{{dy} \over {dx}} = {a^2}$$ ('a' belong a constant) is
WB JEE 2017
GO TO QUESTION
If $$y = {e^{m{{\sin }^{ - 1}}x}}$$ then $$(1 - {x^2}){{{d^2}y} \over {d{x^2}}} - x{{dy} \over {dx}} - $$ky = 0, where k...
WB JEE 2017
GO TO QUESTION
The differential equation of y = aebx (a & b are parameters) is
WB JEE 2011
GO TO QUESTION
Integrating factor (I.F.) of the differential equation $${{dy} \over {dx}} - {{3{x^2}} \over {1 + {x^3}}}y = {{{{\sin }^...
WB JEE 2011
GO TO QUESTION
The solution of $${{dy} \over {dx}} = {y \over x} + \tan {y \over x}$$ is
WB JEE 2011
GO TO QUESTION
he general solution of the differential equation $${\log _e}\left( {{{dy} \over {dx}}} \right) = x + y$$ is
WB JEE 2011
GO TO QUESTION
The degree and order of the differential equation $$y = x{\left( {{{dy} \over {dx}}} \right)^2} + {\left( {{{dx} \over {...
WB JEE 2011
GO TO QUESTION
The general solution of the differential equation $${{{d^2}y} \over {d{x^2}}} + 8{{dy} \over {dx}} + 16y = 0$$ is
WB JEE 2011
GO TO QUESTION
The displacement of a particle at time t is x, where x = t4 $$-$$ kt3. If the velocity of the particle at time t = 2 is ...
WB JEE 2010
GO TO QUESTION
The displacement x of a particle at time t is given by x = At2 + Bt + C, where A, B, C are constants and v is velocity o...
WB JEE 2010
GO TO QUESTION
If the displacement, velocity and acceleration of a particle at time t be x, v and f respectively, then which one is tru...
WB JEE 2010
GO TO QUESTION
Solution of the differential equation xdy $$-$$ ydx = 0 represents a
WB JEE 2010
GO TO QUESTION
The equation of one of the curves whose slope at any point is equal to y + 2x is
WB JEE 2010
GO TO QUESTION
The degree of the differential equation $$x = 1 + \left( {{{dy} \over {dx}}} \right) + {1 \over {2!}}{\left( {{{dy} \ove...
WB JEE 2010
GO TO QUESTION
If $$y'' - 3y' + 2y = 0$$ where y(0) = 1, y'(0) = 0, then the value of y at $$x = {\log _e}2$$ is
WB JEE 2010
GO TO QUESTION
The general solution of the differential equation $$100{{{d^2}y} \over {d{x^2}}} - 20{{dy} \over {dx}} + y = 0$$ is...
WB JEE 2010
GO TO QUESTION
The order of the differential equation $${{{d^2}y} \over {d{x^2}}} = \sqrt {1 + {{\left( {{{dy} \over {dx}}} \right)}^2}...
WB JEE 2009
GO TO QUESTION
If x2 + y2 = 1, then
WB JEE 2009
GO TO QUESTION
The integrating factor of the differential equation $$x\log x{{dy} \over {dx}} + y = 2\log x$$ is given by
WB JEE 2009
GO TO QUESTION
The general solution of the differential equation $${{dy} \over {dx}} = {e^{y + x}} + {e^{y - x}}$$ is where c is an arb...
WB JEE 2009
GO TO QUESTION
The slope at any point of a curve y = f(x) is given by $${{dy} \over {dx}} = 3{x^2}$$ and it passes through ($$-$$1, 1)....
WB JEE 2009
GO TO QUESTION
The differential equation of the family of curves $$y = {e^{2x}}(a\cos x + b\sin x)$$, where a and b are arbitrary const...
WB JEE 2008
GO TO QUESTION
The differential equation of the family of circles passing through the fixed points (a, 0) and ($$-$$a, 0) is
WB JEE 2008
GO TO QUESTION
The order and degree of the following differential equation $${\left[ {1 + {{\left( {{{dy} \over {dx}}} \right)}^2}} \ri...
WB JEE 2008
GO TO QUESTION
The solution of the differential equation $${{dy} \over {dx}} = {e^{y + x}} + {e^{y - x}}$$ is
WB JEE 2008
GO TO QUESTION
The differential equation of all parabolas whose axes are parallel to y-axis is
WB JEE 2008
GO TO QUESTION
The degree of the differential equation $${\left[ {1 + {{\left( {{{dy} \over {dx}}} \right)}^2}} \right]^{5/3}} = {{{d^2...
WB JEE 2008
GO TO QUESTION
Subjective
More
Find the general solution of $$(x + \log y)dy + y\,dx = 0$$
WB JEE 2011
GO TO QUESTION
Let R be the set of real numbers and f : R $$\to$$ R be such that for all x, y $$\in$$ R, $$|f(x) - f(y)| \le |x - y{|^3...
WB JEE 2011
GO TO QUESTION
If $${{dy} \over {dx}} + \sqrt {{{1 - {y^2}} \over {1 - {x^2}}}} = 0$$, prove that $$x\sqrt {1 - {y^2}} + y\sqrt {1 - ...
WB JEE 2010
GO TO QUESTION
If f is differentiable at x = a, find the value of $$\mathop {\lim }\limits_{x \to a} {{{x^2}f(a) - {a^2}f(x)} \over {x ...
WB JEE 2009
GO TO QUESTION
If x = sin t, y = sin 2t, prove that $$(1 - {x^2}){{{d^2}y} \over {d{x^2}}} - x{{dy} \over {dx}} + 4y = 0$$
WB JEE 2009
GO TO QUESTION
Show that sin x is a monotonic increasing function of x in 0
WB JEE 2008
GO TO QUESTION
Joint Entrance Examination
JEE Main
JEE Advanced
WB JEE
Graduate Aptitude Test in Engineering
GATE CSE
GATE ECE
GATE EE
GATE ME
GATE CE
GATE PI
GATE IN
Medical
NEET
CBSE
Class 12