List of top Mathematics Questions on Differential equations asked in JEE Main

Let the solution curve $y = y(x)$ of the differential equation $(1 + e^{2x})\left(\frac{dy}{dx} + y\right) = 1$ pass through the point $(0, \frac{\pi}{2})$. Then, $\lim_{{x \to \infty}} e^x y(x)$ is equal to

Let the solution curve y = y(x) of the differential equation
$[ \frac{x}{\sqrt{x² -y²}} + e^\frac{y}{x} ] x \frac{dy}{dx} = x + [ \frac{x}{\sqrt{x² -y²}} + e^\frac{y}{x} ]y$
pass through the points (1, 0) and (2α, α), α> 0. Then α is equal to

Let ƒ :R→R be a function defined by
$f(x) = \frac{2e^{2x}}{e^{2x} + e^x}$
Then $f\left(\frac{1}{100}\right) + f\left(\frac{2}{100}\right) + f\left(\frac{3}{100}\right) + \ldots + f\left(\frac{99}{100}\right)$
is equal to ________.

Let y = y(x), x > 1, be the solution of the differential equation
$(x-1)\frac{dy}{dx} + 2xy = \frac{1}{x-1}$with $y(2) = \frac{1+e^4}{2e^4}$. If $y(3) = \frac{e^α + 1}{βe^α}$ ,
then the value of α + β is equal to ____.

If the solution curve of the differential equation $((tan−1y)−x)dy=(1+y^2)dx$ passes through the point $(1, 0)$, then the abscissa of the point on the curve whose ordinate is $tan(1)$, is

Let
$S = (0, 2\pi) - \left\{\frac{\pi}{2}, \frac{3\pi}{4}, \frac{3\pi}{2}, \frac{7\pi}{4}\right\}$
. Let y = y(x), x∈S, be the solution curve of the differential equation
$\frac{dy}{dx}=\frac{1}{1+sin⁡2x},y(\frac{π}{4})=\frac{1}{2}$
.If the sum of abscissas of all the points of intersection of the curve y = y(x) with the curve
$y=\sqrt2sin⁡x$ is $\frac{kπ}{12}$,
then k is equal to _________.

Let $y = y(x)$ be the solution of the differential equation $(1 - x^2) \, dy = (xy + (x^3 + 2) \sqrt{1 - x^2}) \, dx \quad -1 < x < 1$, and $y(0) = 0.$ If $\int_{-\frac{1}{2}}^{\frac{1}{2}} \sqrt{1 - x^2} \, y(x) \, dx = k$ then $k^{−1}$ is equal to_______.

Let y = y(x) be the solution curve of the differential equation

$\begin{array}{l} \frac{dy}{dx}+\frac{1}{x^2-1}y=\left(\frac{x-1}{x+1}\right)^{1/2},x>1 \end{array}$

passing through the point (2, √(1/3)). Then √7 y(8) is

The differential equation of the family of circles passing through the points (0, 2) and (0, –2) is

Let x = x(y) be the solution of the differential equation
$2ye^{\frac{x}{y^2}}dx+(y^2−4xe^{\frac{x}{y^2}})dy=0 $
such that x(1) = 0. Then, x(e) is equal to

Let y = y(x) be the solution curve of the differential equation
$\sin(2x^2) \log_e(\tan(x^2)) \,dy + (4xy - 4\sqrt{2}x\sin(x^2 - \frac{\pi}{4})) \,dx = 0, \quad 0 < x < \sqrt{\frac{\pi}{2}}$
which passes through the point $(\sqrt{\frac{π}{6}},1)$. Then $|y(\sqrt{\frac{π}{3}})|$
is equal to _______.