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Differential Equations

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2019
Given that the slope of the tangent to a curve $y=y(x)$ at any point ( $x, y$ ) is $\frac{2 y}{x^2}$. If the curve passes...
JEE Main Mathematics Easy
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Q JEE MAIN 2021 S2
Let a curve $y=f(x)$ pass through the point $\left(2,\left(\log _e 2\right)^2\right)$ and have slope $\frac{2 y}{x \log _e x}$ for all positive real value of...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
Let $y=y(x)$ be the solution of the differential equation $x d y=\left(y+x^3 \cos x\right) d x$ with $y(\pi)=0$, then $y\left(\frac{\pi}{2}\right)$ is equal to:
JEE Main Mathematics Medium
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Q JEE MAIN 2021
If $y=y(x), y \in\left[0, \frac{\pi}{2}\right)$ is the solution of the dirrential equation $\sec y \frac{d y}{d x}-\sin x(x+y)-\sin (x-y)=0$, with $y(0)=$ 0 , then $...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let $F:[3,5] \rightarrow R$ be a twice differentiable function on $(3,5)$ such that
$F(x)=e^{-x} \int_3^x\left(3 t^2+2 t+4 F^{\prime}(t)\right) d t$
If $...
JEE Main Mathematics Hard
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Q JEE MAIN 2021
Let $y=y(x)$ be solution of the differential equation $\log _e\left(\frac{d y}{d x}\right)=3 x+4 y$, with $y(0)=0$. If $y\left(-\frac{2}{3} \log _e 2\right)=\alpha \log _e 2$, then...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
Let $y=y(x)$ be the solution of the differential equation $e^x \sqrt{1-y^2} d x+\left(\frac{y}{x}\right) d y=0, y(1)=-1$. Then the value of $(y(3))^2$ is equal to :
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let $y=y(x)$ be the solution of the differential equation $x \tan \left(\frac{y}{x}\right) d y=\left(y \tan \left(\frac{y}{x}\right)-x\right) d x,-1 \leq x \leq 1, y\left(\frac{1}{2}\right)=\frac{\pi}{6}$. Then the...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
If the curve, $y=y(x)$ represented by the solution of the differential equation $\left(2 x y^2-y\right) d x+x d y=0$, passes through the intersection of the...
JEE Main Mathematics Medium
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Q JEE MAIN_2021_
Let $y=y(x)$ be the solution of the differential equation $\operatorname{cosec}^2 x d y+2 d x=(1+y \cos 2 x) \operatorname{cosec}^2 x d x$, with $\mathrm{y}\left(\frac{\pi}{4}\right)=0$. Then,...
JEE Main Mathematics Easy
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