JEE MAIN Differential Equation Previous Year Questions (PYQs) – Page 1 of 15

Let the population of rabbits surviving at time $t$ be governed by the differential equation $\dfrac{dp(t)}{dt}=\dfrac{1}{2}p(t)-200$. If $p(0)=100$, then $p(t)$ equals:

The curve amongst the family of curves represented by the differential equation $(x^2 - y^2)dx + 2xy\,dy = 0$ which passes through $(1, 1)$ is :

The area enclosed by the closed curve $\mathcal{C}$ given by the differential equation $\dfrac{dy}{dx}+\dfrac{x+a}{\,y-2\,}=0,\quad y(1)=0$ is $4\pi$. Let $P$ and $Q$ be the points of intersection of the curve $\mathcal{C}$ with the $y$-axis. If the normals at $P$ and $Q$ on $\mathcal{C}$ intersect the $x$-axis at points $R$ and $S$ respectively, then the length of the line segment $RS$ is:

Let y = y(x) be the solution of the differential equation xdy = (y + x³ cosx)dx with y($\pi$) = 0, then $y\left( {{\pi \over 2}} \right)$ is equal to :

If $y=y(x)$ is the solution curve of the differential equation $\dfrac{dy}{dx}+y\tan x=x\sec x,\ 0\le x\le \dfrac{\pi}{3},\ y(0)=1$, then $y\!\left(\dfrac{\pi}{6}\right)$ is equal to:

The general solution of the differential equation (y² – x³)dx – xydy = 0 (x $ \ne $ 0) is : (where c is a constant of integration)

If a curve $y=y(x)$ passes through the point $\left(1,\dfrac{\pi}{2}\right)$ and satisfies the differential equation $(7x^{4}\cot y-e^{x}\csc y),\dfrac{dx}{dy}=x^{5},\ x\ge1$, then at $x=2$, the value of $\cos y$ is:

Let the solution curve $y=f(x)$ of the differential equation $\dfrac{dy}{dx}+\dfrac{xy}{x^{2}-1}=\dfrac{x^{4}+2x}{\sqrt{1-x^{2}}}$, $x\in(-1,1)$, pass through the origin. Then $\displaystyle \int_{-\sqrt{3}/2}^{\sqrt{3}/2} f(x)\,dx$ is equal to:

Let $y=y(x)$ be the solution of the differential equation $(x^{2}+4)^{2}\,dy+(2x^{3}y+8xy-2)\,dx=0.$ If $y(0)=0$, then $y(2)$ is equal to:

Let y = y(x) be solution of the differential equation ${\log _{}}\left( {{{dy} \over {dx}}} \right) = 3x + 4y$, with y(0) = 0.If $y\left( { - {2 \over 3}{{\log }_e}2} \right) = \alpha {\log _e}2$, then the value of $\alpha$ is equal to :