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## Differential Equations

### Mathematics

#### Previous Years Questions

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Let $$y=y(x)$$ be the solution curve of the differential equation $$\frac{d y}{d x}+\left(\frac{2 x^{2}+11 x+13}{x^{3}+... JEE Main 2022 (Online) 29th July Evening Shift If the solution curve of the differential equation$$\frac{d y}{d x}=\frac{x+y-2}{x-y}$$passes through the points$$(2,...
JEE Main 2022 (Online) 29th July Evening Shift
Let the solution curve $$y=y(x)$$ of the differential equation $$\left(1+\mathrm{e}^{2 x}\right)\left(\frac{\mathrm{d} y... JEE Main 2022 (Online) 29th July Morning Shift The differential equation of the family of circles passing through the points$$(0,2)$$and$$(0,-2)$$is : JEE Main 2022 (Online) 28th July Evening Shift Let$$y=y(x)$$be the solution curve of the differential equation$$ \frac{d y}{d x}+\frac{1}{x^{2}-1} y=\left(\frac{x-1...
JEE Main 2022 (Online) 28th July Evening Shift
The minimum value of the twice differentiable function $$f(x)=\int\limits_{0}^{x} \mathrm{e}^{x-\mathrm{t}} f^{\prime}(\... JEE Main 2022 (Online) 28th July Morning Shift If$$y=y(x), x \in(0, \pi / 2)$$be the solution curve of the differential equation$$\left(\sin ^{2} 2 x\right) \frac{d...
JEE Main 2022 (Online) 28th July Morning Shift
Let the solution curve of the differential equation $$x \mathrm{~d} y=\left(\sqrt{x^{2}+y^{2}}+y\right) \mathrm{d} x, x>... JEE Main 2022 (Online) 28th July Morning Shift Let$$y=y_{1}(x)$$and$$y=y_{2}(x)$$be two distinct solutions of the differential equation$$\frac{d y}{d x}=x+y$$, wi... JEE Main 2022 (Online) 27th July Morning Shift Let the solution curve$$y=f(x)$$of the differential equation$$ \frac{d y}{d x}+\frac{x y}{x^{2}-1}=\frac{x^{4}+2 x}{\...
JEE Main 2022 (Online) 26th July Evening Shift
If $${{dy} \over {dx}} + 2y\tan x = \sin x,\,0 ... JEE Main 2022 (Online) 26th July Morning Shift The general solution of the differential equation$$\left(x-y^{2}\right) \mathrm{d} x+y\left(5 x+y^{2}\right) \mathrm{d}...
JEE Main 2022 (Online) 25th July Morning Shift
If x = x(y) is the solution of the differential equation $$y{{dx} \over {dy}} = 2x + {y^3}(y + 1){e^y},\,x(1) = 0$$; the...
JEE Main 2022 (Online) 24th June Morning Shift
If the solution curve $$y = y(x)$$ of the differential equation $${y^2}dx + ({x^2} - xy + {y^2})dy = 0$$, which passes t...
JEE Main 2022 (Online) 25th June Morning Shift
Let $$y = y(x)$$ be the solution of the differential equation $$(x + 1)y' - y = {e^{3x}}{(x + 1)^2}$$, with $$y(0) = {1 ... JEE Main 2022 (Online) 25th June Morning Shift Let$$g:(0,\infty ) \to R$$be a differentiable function such that$$\int {\left( {{{x(\cos x - \sin x)} \over {{e^x} + ...
JEE Main 2022 (Online) 25th June Morning Shift
If $$y = y(x)$$ is the solution of the differential equation $$2{x^2}{{dy} \over {dx}} - 2xy + 3{y^2} = 0$$ such that $$... JEE Main 2022 (Online) 25th June Evening Shift If the solution of the differential equation$${{dy} \over {dx}} + {e^x}\left( {{x^2} - 2} \right)y = \left( {{x^2} - 2x...
JEE Main 2022 (Online) 26th June Evening Shift
If $$y = y(x)$$ is the solution of the differential equation $$x{{dy} \over {dx}} + 2y = x\,{e^x}$$, $$y(1) = 0$$ then t...
JEE Main 2022 (Online) 26th June Evening Shift
If $${{dy} \over {dx}} + {{{2^{x - y}}({2^y} - 1)} \over {{2^x} - 1}} = 0$$, x, y > 0, y(1) = 1, then y(2) is equal to :...
JEE Main 2022 (Online) 27th June Morning Shift
If the solution curve of the differential equation $$(({\tan ^{ - 1}}y) - x)dy = (1 + {y^2})dx$$ passes through the poin...
JEE Main 2022 (Online) 27th June Evening Shift
Let y = y(x) be the solution of the differential equation $$x(1 - {x^2}){{dy} \over {dx}} + (3{x^2}y - y - 4{x^3}) = 0$$...
JEE Main 2022 (Online) 28th June Morning Shift
Let the solution curve $$y = y(x)$$ of the differential equation $$\left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \... JEE Main 2022 (Online) 28th June Morning Shift Let x = x(y) be the solution of the differential equation$$2y\,{e^{x/{y^2}}}dx + \left( {{y^2} - 4x{e^{x/{y^2}}}} \righ...
JEE Main 2022 (Online) 28th June Evening Shift
If y = y(x) is the solution of the differential equation $$\left( {1 + {e^{2x}}} \right){{dy} \over {dx}} + 2\left( {1 +... JEE Main 2022 (Online) 29th June Evening Shift Let the solution curve of the differential equation$$x{{dy} \over {dx}} - y = \sqrt {{y^2} + 16{x^2}} $$,$$y(1) = 3$$... JEE Main 2022 (Online) 29th June Morning Shift If y = y(x) is the solution curve of the differential equation$${x^2}dy + \left( {y - {1 \over x}} \right)dx = 0$$; x ... JEE Main 2021 (Online) 1st September Evening Shift If$$y{{dy} \over {dx}} = x\left[ {{{{y^2}} \over {{x^2}}} + {{\phi \left( {{{{y^2}} \over {{x^2}}}} \right)} \over {\ph...
JEE Main 2021 (Online) 31st August Evening Shift
If $${{dy} \over {dx}} = {{{2^x}y + {2^y}{{.2}^x}} \over {{2^x} + {2^{x + y}}{{\log }_e}2}}$$, y(0) = 0, then for y = 1,...
JEE Main 2021 (Online) 31st August Evening Shift
If $${{dy} \over {dx}} = {{{2^{x + y}} - {2^x}} \over {{2^y}}}$$, y(0) = 1, then y(1) is equal to :
JEE Main 2021 (Online) 31st August Morning Shift
If the solution curve of the differential equation (2x $$-$$ 10y3)dy + ydx = 0, passes through the points (0, 1) and (2,...
JEE Main 2021 (Online) 27th August Evening Shift
A differential equation representing the family of parabolas with axis parallel to y-axis and whose length of latus rect...
JEE Main 2021 (Online) 27th August Evening Shift
Let us consider a curve, y = f(x) passing through the point ($$-$$2, 2) and the slope of the tangent to the curve at any...
JEE Main 2021 (Online) 27th August Morning Shift
Let y = y(x) be the solution of the differential equation $${{dy} \over {dx}} = 2(y + 2\sin x - 5)x - 2\cos x$$ such tha...
JEE Main 2021 (Online) 27th August Morning Shift
Let y(x) be the solution of the differential equation 2x2 dy + (ey $$-$$ 2x)dx = 0, x &gt; 0. If y(e) = 1, then y(1) is ...
JEE Main 2021 (Online) 26th August Evening Shift
Let y = y(x) be a solution curve of the differential equation $$(y + 1){\tan ^2}x\,dx + \tan x\,dy + y\,dx = 0$$, $$x \i... JEE Main 2021 (Online) 26th August Morning Shift Let y = y(x) be solution of the differential equation$${\log _{}}\left( {{{dy} \over {dx}}} \right) = 3x + 4y$$, with y... JEE Main 2021 (Online) 27th July Morning Shift Let y = y(x) be the solution of the differential equation xdy = (y + x3 cosx)dx with y($$\pi$$) = 0, then$$y\left( {{\p...
JEE Main 2021 (Online) 25th July Evening Shift
Let y = y(x) be the solution of the differential equation (x $$-$$ x3)dy = (y + yx2 $$-$$ 3x4)dx, x &gt; 2. If y(3) = 3,...
JEE Main 2021 (Online) 27th July Evening Shift
Let y = y(x) be the solution of the differential equation $${{dy} \over {dx}} = 1 + x{e^{y - x}}, - \sqrt 2 &lt; x &lt;... JEE Main 2021 (Online) 25th July Morning Shift Let y = y(x) be the solution of the differential equation$$\cos e{c^2}xdy + 2dx = (1 + y\cos 2x)\cos e{c^2}xdx$$, with ... JEE Main 2021 (Online) 22th July Evening Shift Let y = y(x) be the solution of the differential equation$${e^x}\sqrt {1 - {y^2}} dx + \left( {{y \over x}} \right)dy =...
JEE Main 2021 (Online) 20th July Morning Shift
Let y = y(x) be the solution of the differential equation $$x\tan \left( {{y \over x}} \right)dy = \left( {y\tan \left( ... JEE Main 2021 (Online) 20th July Morning Shift Let y = y(x) be the solution of the differential equation$${{dy} \over {dx}} = (y + 1)\left( {(y + 1){e^{{x^2}/2}} - x}...
JEE Main 2021 (Online) 18th March Evening Shift
The differential equation satisfied by the system of parabolas y2 = 4a(x + a) is :
JEE Main 2021 (Online) 18th March Morning Shift
Let y = y(x) be the solution of the differential equation $$\cos x(3\sin x + \cos x + 3)dy = (1 + y\sin x(3\sin x + \cos... JEE Main 2021 (Online) 17th March Evening Shift If the curve y = y(x) is the solution of the differential equation$$2({x^2} + {x^{5/4}})dy - y(x + {x^{1/4}})dx = {2^{9...
JEE Main 2021 (Online) 17th March Evening Shift
Which of the following is true for y(x) that satisfies the differential equation $${{dy} \over {dx}}$$ = xy $$-$$ 1 + x ...
JEE Main 2021 (Online) 17th March Morning Shift
Let C1 be the curve obtained by the solution of differential equation $$2xy{{dy} \over {dx}} = {y^2} - {x^2},x &gt; 0$$....
JEE Main 2021 (Online) 16th March Evening Shift
If y = y(x) is the solution of the differential equation $${{dy} \over {dx}}$$ + (tan x) y = sin x, $$0 \le x \le {\pi ... JEE Main 2021 (Online) 16th March Evening Shift If y = y(x) is the solution of the differential equation,$${{dy} \over {dx}} + 2y\tan x = \sin x,y\left( {{\pi \over 3...
JEE Main 2021 (Online) 16th March Morning Shift
Let $$f(x) = \int\limits_0^x {{e^t}f(t)dt + {e^x}}$$ be a differentiable function for all x$$\in$$R. Then f(x) equals :
JEE Main 2021 (Online) 26th February Evening Shift
The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is ...
JEE Main 2021 (Online) 26th February Morning Shift
If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is $${{{x^2} - 4x + y + 8} \... JEE Main 2021 (Online) 25th February Morning Slot The population P = P(t) at time 't' of a certain species follows the differential equation$${{dP} \over {dt}}$$= 0.5P ... JEE Main 2021 (Online) 24th February Morning Slot If$$y = \left( {{2 \over \pi }x - 1} \right) cosec\,x$$is the solution of the differential equation,$${{dy} \over {d...
JEE Main 2020 (Online) 6th September Evening Slot
The general solution of the differential equation $$\sqrt {1 + {x^2} + {y^2} + {x^2}{y^2}}$$ + xy$${{dy} \over {dx}}$$ ...
JEE Main 2020 (Online) 6th September Morning Slot
Let y = y(x) be the solution of the differential equation cosx$${{dy} \over {dx}}$$ + 2ysinx = sin2x, x $$\in$$ $$\lef... JEE Main 2020 (Online) 5th September Evening Slot If y = y(x) is the solution of the differential equation$${{5 + {e^x}} \over {2 + y}}.{{dy} \over {dx}} + {e^x} = 0$$... JEE Main 2020 (Online) 5th September Morning Slot The solution of the differential equation$${{dy} \over {dx}} - {{y + 3x} \over {{{\log }_e}\left( {y + 3x} \right)}} +...
JEE Main 2020 (Online) 4th September Evening Slot
Let f be a twice differentiable function on (1, 6). If f(2) = 8, f’(2) = 5, f’(x) $$\ge$$ 1 and f''(x) $$\ge$$ 4, fo...
JEE Main 2020 (Online) 4th September Morning Slot
Let y = y(x) be the solution of the differential equation, xy'- y = x2(xcosx + sinx), x &gt; 0. if y ($$\pi$$) = $$\pi ... JEE Main 2020 (Online) 4th September Morning Slot The solution curve of the differential equation, (1 + e-x)(1 + y2)$${{dy} \over {dx}}$$= y2, which passes through the p... JEE Main 2020 (Online) 3rd September Morning Slot If a curve y = f(x), passing through the point (1, 2), is the solution of the differential equation, 2x2dy= (2xy + y2)dx... JEE Main 2020 (Online) 2nd September Evening Slot If$${{dy} \over {dx}} = {{xy} \over {{x^2} + {y^2}}}$$; y(1) = 1; then a value of x satisfying y(x) = e is : JEE Main 2020 (Online) 9th January Evening Slot The differential equation of the family of curves, x2 = 4b(y + b), b$$ \in $$R, is JEE Main 2020 (Online) 8th January Evening Slot Let y = y(x) be a solution of the differential equation,$$\sqrt {1 - {x^2}} {{dy} \over {dx}} + \sqrt {1 - {y^2}} = 0$... JEE Main 2020 (Online) 8th January Morning Slot Let y = y(x) be the solution curve of the differential equation, $$\left( {{y^2} - x} \right){{dy} \over {dx}} = 1$$, sa... JEE Main 2020 (Online) 7th January Evening Slot If y = y(x) is the solution of the differential equation, $${e^y}\left( {{{dy} \over {dx}} - 1} \right) = {e^x}$$ such t... JEE Main 2020 (Online) 7th January Morning Slot Let xk + yk = ak, (a, k &gt; 0 ) and $${{dy} \over {dx}} + {\left( {{y \over x}} \right)^{{1 \over 3}}} = 0$$, then k is... JEE Main 2020 (Online) 7th January Morning Slot The general solution of the differential equation (y2 – x3)dx – xydy = 0 (x $$\ne$$ 0) is : (where c is a constant of ... JEE Main 2019 (Online) 12th April Evening Slot Consider the differential equation, $${y^2}dx + \left( {x - {1 \over y}} \right)dy = 0$$, If value of y is 1 when x = 1,... JEE Main 2019 (Online) 12th April Morning Slot Let y = y(x) be the solution of the differential equation, $${{dy} \over {dx}} + y\tan x = 2x + {x^2}\tan x$$, $$x \in \... JEE Main 2019 (Online) 10th April Evening Slot If y = y(x) is the solution of the differential equation$${{dy} \over {dx}} = \left( {\tan x - y} \right){\sec ^2}x$$,... JEE Main 2019 (Online) 10th April Morning Slot If$$\cos x{{dy} \over {dx}} - y\sin x = 6x$$, (0 &lt; x &lt;$${\pi \over 2}$$) and$$y\left( {{\pi \over 3}} \right)... JEE Main 2019 (Online) 9th April Evening Slot The solution of the differential equation $$x{{dy} \over {dx}} + 2y$$ = x2 (x $$\ne$$ 0) with y(1) = 1, is... JEE Main 2019 (Online) 9th April Morning Slot Let y = y(x) be the solution of the differential equation, $${({x^2} + 1)^2}{{dy} \over {dx}} + 2x({x^2} + 1)y = 1$$ suc... JEE Main 2019 (Online) 8th April Morning Slot If a curve passes through the point (1, –2) and has slope of the tangent at any point (x, y) on it as $${{{x^2} - 2y} \o... JEE Main 2019 (Online) 12th January Evening Slot Let y = y(x) be the solution of the differential equation, x$${{dy} \over {dx}}$$+ y = x loge x, (x &gt; 1). If 2y(2)... JEE Main 2019 (Online) 12th January Morning Slot The solution of the differential equation,$${{dy} \over {dx}}$$= (x – y)2, when y(1) = 1, is : JEE Main 2019 (Online) 11th January Evening Slot If &nbsp;xloge(logex)$$-$$x2 + y2 = 4(y &gt; 0), then$${{dy} \over {dx}}$$at x = e is equal to : ... JEE Main 2019 (Online) 11th January Morning Slot A helicopter is flying along the curve given by y – x3/2 = 7, (x$$ \ge $$0). A soldier positioned at the point$$\left... JEE Main 2019 (Online) 10th January Evening Slot Let f be a differentiable function such that f '(x) = 7 - $${3 \over 4}{{f\left( x \right)} \over x},$$ (x &gt; 0) and f... JEE Main 2019 (Online) 10th January Evening Slot The curve amongst the family of curves represented by the differential equation, (x2 – y2)dx + 2xy dy = 0 which passes t... JEE Main 2019 (Online) 10th January Evening Slot Let f : [0,1] $$\to$$&nbsp;R be such that f(xy) = f(x).f(y), for all x, y $$\in$$ [0, 1], and f(0) $$\ne$$ 0. If ... JEE Main 2019 (Online) 9th January Evening Slot The maximum volume (in cu.m) of the right circular cone having slant height 3 m is : JEE Main 2019 (Online) 9th January Morning Slot If y = y(x) is the solution of the differential equation, x$$dy \over dx$$ + 2y = x2, satisfying y(1) = 1, then y($$1\o... JEE Main 2019 (Online) 9th January Morning Slot The differential equation representing the family of ellipse having foci eith on the x-axis or on the$$y$$-axis, center... JEE Main 2018 (Online) 16th April Morning Slot The curve satifying the differeial equation, (x2$$-$$y2) dx + 2xydy = 0 and passing through the point (1, 1) is : ... JEE Main 2018 (Online) 15th April Evening Slot Let y = y(x) be the solution of the differential equation$${{dy} \over {dx}} + 2y = f\left( x \right),$$where$$f\left... JEE Main 2018 (Online) 15th April Morning Slot Let y = y(x) be the solution of the differential equation $$\sin x{{dy} \over {dx}} + y\cos x = 4x$$, $$x \in \left( {0,... JEE Main 2018 (Offline) Let S = { t$$ \in R:f(x) = \left| {x - \pi } \right|.\left( {{e^{\left| x \right|}} - 1} \right)\sin \left| x \righ... JEE Main 2018 (Offline) Let $$f\left( x \right) = {x^2} + {1 \over {{x^2}}}$$ and $$g\left( x \right) = x - {1 \over x}$$, $$x \in R - \left\{ {... JEE Main 2018 (Offline) If the curves y2 = 6x, 9x2 + by2 = 16 intersect each other at right angles, then the value of b is :... JEE Main 2018 (Offline) The curve satisfying the differential equation, ydx$$-$$(x + 3y2)dy = 0 and passing through the point (1, 1), also pas... JEE Main 2017 (Online) 8th April Morning Slot If$$\left( {2 + \sin x} \right){{dy} \over {dx}} + \left( {y + 1} \right)\cos x = 0$$and y(0) = 1, then$$y\left( {{\p... JEE Main 2017 (Offline) Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area ... JEE Main 2017 (Offline) The normal to the curve y(x – 2)(x – 3) = x + 6 at the point where the curve intersects the y-axis passes through the po... JEE Main 2017 (Offline) The solution of the differential equation $${{dy} \over {dx}}\, + \,{y \over 2}\,\sec x = {{\tan x} \over {2y}},\,\,$$ ... JEE Main 2016 (Online) 10th April Morning Slot If&nbsp;&nbsp; f(x) is a differentiable function in the interval (0, $$\infty$$) such that f (1) = 1 and $$\mathop {... JEE Main 2016 (Online) 9th April Morning Slot If a curve$$y=f(x)$$passes through the point$$(1,-1)$$and satisfies the differential equation,$$y(1+xy) dx=xdy... JEE Main 2016 (Offline) Let $$y(x)$$ be the solution of the differential equation $$\left( {x\,\log x} \right){{dy} \over {dx}} + y = 2x\,\log ... JEE Main 2015 (Offline) Let the population of rabbits surviving at time$$t$$be governed by the differential equation$${{dp\left( t \right)} ... JEE Main 2014 (Offline) At present, a firm is manufacturing $$2000$$ items. It is estimated that the rate of change of production P w.r.t. add... JEE Main 2013 (Offline) The population $$p$$ $$(t)$$ at time $$t$$ of a certain mouse species satisfies the differential equation $${{dp\left( t... AIEEE 2012 If$${{dy} \over {dx}} = y + 3 &gt; 0\,\,$$and$$y(0)=2,$$then$$y\left( {\ln 2} \right)$$is equal to : AIEEE 2011 Let$$I$$be the purchase value of an equipment and$$V(t)$$be the value after it has been used for$$t$$years. The va... AIEEE 2011 Solution of the differential equation$$\cos x\,dy = y\left( {\sin x - y} \right)dx,\,\,0 &lt; x{\pi \over 2}$$is ... AIEEE 2010 The differential equation which represents the family of curves$$y = {c_1}{e^{{c_2}x}},$$where$${c_1}$$, and$${c_2}... AIEEE 2009 The solution of the differential equation $${{dy} \over {dx}} = {{x + y} \over x}$$ satisfying the condition $$y(1)=1$$... AIEEE 2008 The differential equation of all circles passing through the origin and having their centres on the $$x$$-axis is AIEEE 2007 The differential equation whose solution is $$A{x^2} + B{y^2} = 1$$ where $$A$$ and $$B$$ are arbitrary constants is of... AIEEE 2006 If $$x{{dy} \over {dx}} = y\left( {\log y - \log x + 1} \right),$$ then the solution of the equation is AIEEE 2005 The differential equation representing the family of curves $${y^2} = 2c\left( {x + \sqrt c } \right),$$ where $$c&gt;0,... AIEEE 2005 Solution of the differential equation$$ydx + \left( {x + {x^2}y} \right)dy = 0$$is AIEEE 2004 The differential equation for the family of circle$${x^2} + {y^2} - 2ay = 0,$$where a is an arbitrary constant is AIEEE 2004 The degree and order of the differential equation of the family of all parabolas whose axis is$$x$$-axis, are respectiv... AIEEE 2003 The solution of the differential equation$$\left( {1 + {y^2}} \right) + \left( {x - {e^{{{\tan }^{ - 1}}y}}} \right){{... AIEEE 2003 The solution of the equation $$\,{{{d^2}y} \over {d{x^2}}} = {e^{ - 2x}}$$ AIEEE 2002 The order and degree of the differential equation $$\,{\left( {1 + 3{{dy} \over {dx}}} \right)^{2/3}} = 4{{{d^3}y} \ove... AIEEE 2002 ## Numerical More Let$$y=y(x)$$be the solution curve of the differential equation$$\sin \left( {2{x^2}} \right){\log _e}\left( {\tan {x... JEE Main 2022 (Online) 27th July Morning Shift Suppose $$y=y(x)$$ be the solution curve to the differential equation $$\frac{d y}{d x}-y=2-e^{-x}$$ such that $$\lim\li... JEE Main 2022 (Online) 26th July Evening Shift Let$$f$$be a twice differentiable function on$$\mathbb{R}$$. If$$f^{\prime}(0)=4$$and$$f(x) + \int\limits_0^x {(x ... JEE Main 2022 (Online) 25th July Evening Shift Let $$y=y(x)$$ be the solution of the differential equation $$\frac{d y}{d x}=\frac{4 y^{3}+2 y x^{2}}{3 x y^{2}+x^{3}},... JEE Main 2022 (Online) 25th July Evening Shift Let$$S = (0,2\pi ) - \left\{ {{\pi \over 2},{{3\pi } \over 4},{{3\pi } \over 2},{{7\pi } \over 4}} \right\}$$. Let$$y... JEE Main 2022 (Online) 26th June Morning Shift Let the solution curve y = y(x) of the differential equation $$(4 + {x^2})dy - 2x({x^2} + 3y + 4)dx = 0$$ pass through t... JEE Main 2022 (Online) 26th June Morning Shift Let $$y = y(x)$$ be the solution of the differential equation $$(1 - {x^2})dy = \left( {xy + ({x^3} + 2)\sqrt {1 - {x^2}... JEE Main 2022 (Online) 27th June Evening Shift Let y = y(x), x > 1, be the solution of the differential equation$$(x - 1){{dy} \over {dx}} + 2xy = {1 \over {x - 1}}$$... JEE Main 2022 (Online) 29th June Evening Shift Let y = y(x) be the solution of the differential equation$${{dy} \over {dx}} + {{\sqrt 2 y} \over {2{{\cos }^4}x - {{\c... JEE Main 2022 (Online) 29th June Morning Shift If $${y^{1/4}} + {y^{ - 1/4}} = 2x$$, and $$({x^2} - 1){{{d^2}y} \over {d{x^2}}} + \alpha x{{dy} \over {dx}} + \beta y =... JEE Main 2021 (Online) 27th August Morning Shift If$$y = y(x),y \in \left[ {0,{\pi \over 2}} \right)$$is the solution of the differential equation$$\sec y{{dy} \over... JEE Main 2021 (Online) 27th July Morning Shift Let $$F:[3,5] \to R$$ be a twice differentiable function on (3, 5) such that $$F(x) = {e^{ - x}}\int\limits_3^x {(3{t^2}... JEE Main 2021 (Online) 27th July Morning Shift Let y = y(x) be the solution of the differential equation dy = e$$\alpha$$x + y dx;$$\alpha\in$$N. If y(loge2) = ... JEE Main 2021 (Online) 27th July Evening Shift Let y = y(x) be solution of the following differential equation$${e^y}{{dy} \over {dx}} - 2{e^y}\sin x + \sin x{\cos ^2... JEE Main 2021 (Online) 25th July Morning Shift Let y = y(x) be the solution of the differential equation $$\left( {(x + 2){e^{\left( {{{y + 1} \over {x + 2}}} \right)}... JEE Main 2021 (Online) 22th July Evening Shift Let a curve y = y(x) be given by the solution of the differential equation$$\cos \left( {{1 \over 2}{{\cos }^{ - 1}}({e... JEE Main 2021 (Online) 20th July Evening Shift Let y = y(x) be the solution of the differential equation xdy $$-$$ ydx = $$\sqrt {({x^2} - {y^2})} dx$$, x $$\ge$$ 1,... JEE Main 2021 (Online) 18th March Evening Shift If y = y(x) is the solution of the equation $${e^{\sin y}}\cos y{{dy} \over {dx}} + {e^{\sin y}}\cos x = \cos x$$, y(0) ... JEE Main 2021 (Online) 26th February Morning Shift The difference between degree and order of a differential equation that represents the family of curves given by $${y^2}... JEE Main 2021 (Online) 26th February Morning Shift If the curve, y = y(x) represented by the solution of the differential equation (2xy2$$-$$y)dx + xdy = 0, passes throu... JEE Main 2021 (Online) 25th February Evening Shift If for x$$ \ge$\$ 0, y = y(x) is the solution of the differential equation (x + 1)dy = ((x + 1)2 + y – 3)dx, y(2) = 0, ...
JEE Main 2020 (Online) 9th January Morning Slot

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