Differential Equations PYQs - Last 10 Years
JEE Main / Mathematics / Calculus / 224 recent questions
MathematicsCalculus2017-2026
Practice 224 JEE Main Mathematics questions from Differential Equations. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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Mathematics / Calculus
2017-2026
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143
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224
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2017-2026
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224PYQs
MCQ76.8%
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#2 Hard43
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143 in last 5 years224 in last 10 years
Last 10 Years Differential Equations Questions
Showing 24 of 224 filtered questions.
1Differential Equations
If a curve y = f(x), passing through the point
(1, 2), is the solution of the differential equation,
2x2dy= (2xy + y2)dx, then \(f\left( {{1 \over 2}} \right)\) is equal to :
(1, 2), is the solution of the differential equation,
2x2dy= (2xy + y2)dx, then \(f\left( {{1 \over 2}} \right)\) is equal to :
MCQ+4 / -12020
2Differential Equations
If y = y(x) is the solution of the differential equation,
x\(dy \over dx\) + 2y = x2, satisfying y(1) = 1, then y(\(1\over2\)) is equal
to :
x\(dy \over dx\) + 2y = x2, satisfying y(1) = 1, then y(\(1\over2\)) is equal
to :
MCQ+4 / -12019
3Differential Equations
Let f : [0,1] \(\to\) R be such that f(xy) = f(x).f(y), for all x, y \(\in\) [0, 1], and f(0) \(\ne\) 0. If y = y(x) satiesfies the differential equation, \({{dy} \over {dx}}\) = f(x) with y(0) = 1, then y$$\left( {{1 \over 4}} \righ...
MCQ+4 / -12019
4Differential Equations
The solution of the differential equation
\(x{{dy} \over {dx}} + 2y\) = x2 (x \(\ne\) 0) with y(1) = 1, is :
\(x{{dy} \over {dx}} + 2y\) = x2 (x \(\ne\) 0) with y(1) = 1, is :
MCQ+4 / -12019
5Differential Equations
If \(\cos x{{dy} \over {dx}} - y\sin x = 6x\), (0 < x < \({\pi \over 2}\))
and \(y\left( {{\pi \over 3}} \right)\) = 0 then \(y\left( {{\pi \over 6}} \right)\) is equal to :-
and \(y\left( {{\pi \over 3}} \right)\) = 0 then \(y\left( {{\pi \over 6}} \right)\) is equal to :-
MCQ+4 / -12019
6Differential Equations
Let y = y(x) be the solution of the differential equation, \({({x^2} + 1)^2}{{dy} \over {dx}} + 2x({x^2} + 1)y = 1\) such
that y(0) = 0. If \(\sqrt ay(1)\) = \(\pi \over 32\) , then the value of
'a' is :
that y(0) = 0. If \(\sqrt ay(1)\) = \(\pi \over 32\) , then the value of
'a' is :
MCQ+4 / -12019
7Differential Equations
Let y = y(x) be the solution of the differential equation, x\({{dy} \over {dx}}\) + y = x loge x, (x > 1). If 2y(2) = loge 4 \(-\) 1, then y(e) is equal to :
MCQ+4 / -12019
8Differential Equations
If a curve passes through the point (1, –2) and has slope of the tangent at any point (x, y) on it as \({{{x^2} - 2y} \over x}\), then the curve also passes through the point :
MCQ+4 / -12019
9Differential Equations
Consider the differential equation, \({y^2}dx + \left( {x - {1 \over y}} \right)dy = 0\), If value of y is 1 when x = 1, then the value of x
for which y = 2, is :
for which y = 2, is :
MCQ+4 / -12019
10Differential Equations
The general solution of the differential equation (y2
– x3)dx – xydy = 0 (x \(\ne\) 0) is :
(where c is a constant of integration)
– x3)dx – xydy = 0 (x \(\ne\) 0) is :
(where c is a constant of integration)
MCQ+4 / -12019
11Differential Equations
If y(x) is the solution of the differential equation \({{dy} \over {dx}} + \left( {{{2x + 1} \over x}} \right)y = {e^{ - 2x}},\,\,x > 0,\,\) where \(y\left( 1 \right) = {1 \over 2}{e^{ - 2}},\) then
MCQ+4 / -12019
12Differential Equations
The solution of the differential equation,
\({{dy} \over {dx}}\) = (x – y)2, when y(1) = 1, is :
\({{dy} \over {dx}}\) = (x – y)2, when y(1) = 1, is :
MCQ+4 / -12019
13Differential Equations
If \({{dy} \over {dx}} + {3 \over {{{\cos }^2}x}}y = {1 \over {{{\cos }^2}x}},\,\,x \in \left( {{{ - \pi } \over 3},{\pi \over 3}} \right)\) and \(y\left( {{\pi \over 4}} \right) = {4 \over 3},\) then $$y\left( { - {\pi \over 4}} \r...
MCQ+4 / -12019
14Differential Equations
Let f be a differentiable function such that f '(x) = 7 - \({3 \over 4}{{f\left( x \right)} \over x},\) (x > 0) and f(1) \(\ne\) 4. Then \(\mathop {\lim }\limits_{x \to 0'} \,\) xf\(\left( {{1 \over x}} \right)\) :
MCQ+4 / -12019
15Differential Equations
The curve amongst the family of curves represented by the differential equation, (x2 – y2)dx + 2xy dy = 0 which passes through (1, 1) is :
MCQ+4 / -12019
16Differential Equations
If y = y(x) is the solution of the differential equation
\({{dy} \over {dx}} = \left( {\tan x - y} \right){\sec ^2}x\), \(x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)\),
such that y (0) = 0, then $$y\left( { - {\pi \over 4}} \r...
\({{dy} \over {dx}} = \left( {\tan x - y} \right){\sec ^2}x\), \(x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)\),
such that y (0) = 0, then $$y\left( { - {\pi \over 4}} \r...
MCQ+4 / -12019
17Differential Equations
Let y = y(x) be the solution of the differential equation,
\({{dy} \over {dx}} + y\tan x = 2x + {x^2}\tan x\), \(x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)\), such that
y(0) = 1. Then :
\({{dy} \over {dx}} + y\tan x = 2x + {x^2}\tan x\), \(x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)\), such that
y(0) = 1. Then :
MCQ+4 / -12019
18Differential Equations
The differential equation representing the family of ellipse having foci eith on the x-axis or on the \(y\)-axis, center at the origin and passing through the point (0, 3) is :
MCQ+4 / -12018
19Differential Equations
Let y = y(x) be the solution of the differential equation \({{dy} \over {dx}} + 2y = f\left( x \right),\) where \(f\left( x \right) = \left\{ {\matrix{
{1,} & {x \in \left[ {0,1} \right]} \cr
{0,} & {otherwise} \cr
} } \right.\)...
MCQ+4 / -12018
20Differential Equations
The curve satifying the differeial equation, (x2 \(-\) y2) dx + 2xydy = 0 and passing through the point (1, 1) is :
MCQ+4 / -12018
21Differential Equations
Let y = y(x) be the solution of the differential equation
\(\sin x{{dy} \over {dx}} + y\cos x = 4x\), \(x \in \left( {0,\pi } \right)\).
If \(y\left( {{\pi \over 2}} \right) = 0\), then \(y\left( {{\pi \over 6}} \right)\) is equal to :
\(\sin x{{dy} \over {dx}} + y\cos x = 4x\), \(x \in \left( {0,\pi } \right)\).
If \(y\left( {{\pi \over 2}} \right) = 0\), then \(y\left( {{\pi \over 6}} \right)\) is equal to :
MCQ+4 / -12018
22Differential Equations
If 2x = y\({^{{1 \over 5}}}\) + y\({^{ - {1 \over 5}}}\) and
(x2 \(-\) 1) \({{{d^2}y} \over {d{x^2}}}\) + \(\lambda\)x \({{dy} \over {dx}}\) + ky = 0,
then \(\lambda\) + k is equal to :
(x2 \(-\) 1) \({{{d^2}y} \over {d{x^2}}}\) + \(\lambda\)x \({{dy} \over {dx}}\) + ky = 0,
then \(\lambda\) + k is equal to :
MCQ+4 / -12017
23Differential Equations
The curve satisfying the differential equation, ydx \(-\)(x + 3y2)dy = 0 and passing through the point (1, 1), also passes through the point :
MCQ+4 / -12017
24Differential Equations
If \(\left( {2 + \sin x} \right){{dy} \over {dx}} + \left( {y + 1} \right)\cos x = 0\) and y(0) = 1,
then \(y\left( {{\pi \over 2}} \right)\) is equal to :
then \(y\left( {{\pi \over 2}} \right)\) is equal to :
MCQ+4 / -12017