Differential Equations

Q JEE MAIN 2023

If the solution curve of the differential equation $\left(y-2 \log _e x\right) d x+\left(x \log _e x^2\right) d y=0, x>1$ passes through the points $...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

Let $y=y(x)$ be a solution curve of the differential equation, $\left(1-x^2 y^2\right) d x=y d x+x d y$. If the line $x=1$ intersects the curve...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

Let $f:[2,4] \rightarrow \mathbb{R}$ be a differentiable function such that $\left(x \log _e x\right) f(x)+\left(\log _e x\right) f(x)+f(x) \geq 1, x \in[2,4]$ with $f(2)=\frac{1}{2}$ and...

JEE Main Mathematics Hard

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Q JEE MAIN 2023

Let $y=y(x), y>0$, be a solution curve of the differential equation $\left(1+x^2\right) d y=y(x-y) d x$. If $y(0)=1$ and $y(2 \sqrt{2})=\beta$, then

JEE Main Mathematics Medium

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Q JEE-Main 2023

Let y = y(x) be a solution of the differential equation (xcos x)dy + (xysinx + ycos x – l)dx = 0, 0

JEE Main Mathematics Medium

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Q JEE MAIN 2023

The slope of tangent at any point $(x, y)$ on a curve $y=y(x)$ is $\frac{x^2+y^2}{2 x y}, x>0$. If $y(2)=0$, then a value of $x(8)$...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

Let $f$ be a differentiable function such that $x^2 f(x)-x=4 \int_0^x t f(t) d t, f(1)=\frac{2}{3}$. Then $18 f(3)$ is equal to

JEE Main Mathematics Medium

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Q JEE MAIN

The solution of the differential equation $\left(x^2+y^2\right) d x-5 x y d y=0, y(1)=0$, is :

JEE Main Mathematics Easy

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Q JEE-Main 2024

Let a conic C pass through the point (4,-2) and P(x,y),x≥3, be any point on C. Let the slope of the line touching the conic...

JEE Main Mathematics Easy

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Q JEE MAIN 2024

Let $f$ be a differentiable function in the interval $(0, \infty)$ such that $f(1)=1$ and $\lim _{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1$ for each $x>0$....

JEE Main Mathematics Medium

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