Differential Equations

Q JEE MAIN 2019

Let $y=y(x)$ be the solution of the differential equation, $\left(x^2+1\right)^2 \frac{d y}{d x}+2 x\left(x^2+1\right) y=1$ such that $y(0)=0$. If $\sqrt{a} y(1)=\frac{\pi}{32}$, then the value of...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

Let $y(x)$ be the solution of the differential equation $2 x^2 d y+\left(e^y-2 x\right) d x=0, x>0$. If $y(e)=1$, then $y(1)$ is equal to:

JEE Main Mathematics Medium

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Q JEE MAIN 2021

If $y=y(x)$ is the solution curve of the differential equation $x^2 d y+\left(y-\frac{1}{x}\right) d x=0 ; x>0$ and $y(1)=1$, then $\left(\frac{1}{2}\right)$ is equal to :

JEE Main Mathematics Hard

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Q _JEE MAIN_2021

Let $y=y(x)$ be solution of the following differential equation $e^y \frac{d y}{d x}-2 e^y \sin x+\sin x \cos ^2 x=0, y\left(\frac{\pi}{2}\right)=0$. If $y(0)=\log _0\left(\alpha+\beta e^{-2}\right)$...

JEE Main Mathematics Easy

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Q JEE MAIN 2021 S2

Let $y=y(x)$ be the solution of the differential equation $d y=e^{\alpha x+y} d x ; \alpha \in N$. If $y\left(\log _e 2\right)=\log _e 2$ and...

JEE Main Mathematics Easy

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Q JEE MAIN_2021

Let $y=y(x)$ be the solution of the differential equation $\frac{d}{d x}=1+x e^{y-x},-\sqrt{2}

JEE Main Mathematics Medium

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Q JEE MAIN 2021 S2

Let $y=y(x)$ be the solution of the differential equation $\left(x-x^3\right) d y=\left(y+y x^2-3 x^4\right) d x, x>2$. If $y(3)=3$, then $y(4)$ is equal to:

JEE Main Mathematics Hard

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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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