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Differential Equations

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2020
Let $y=y(x)$ be the solution of the differential equation, $x y^{\prime}-y=x^2(x \cos x+\sin x), x>0$. If $y(\pi)=\pi$, then $y^{\prime \prime}\left(\frac{\pi}{2}\right)+y\left(\frac{\pi}{2}\right)$ is equal to :
JEE Main Mathematics Medium
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Q JEE MAIN 2020
The solution of the dif ferential equation $\frac{d y}{d x}-\frac{y+3 x}{\log _e(y+3 x)}+3=0$ is (where C is a constant of integration.)
JEE Main Mathematics Easy
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Q JEE MAIN 2020
If $\frac{d y}{d x}=\frac{x y}{x^2+y^2} ; y(1)=1 ; \quad$ then a value of $x$ satisfying $y(x)=e$ is :
JEE Main Mathematics Easy
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Q JEE-MAIN 2020
If $x^3 d y+x y d x=x^2 d y+2 y d x ; x(2)=e$ and $x>1$, then $x(4)$ is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN 2019
Let $f:[0,1] \rightarrow R$ be such that $f(x y)=f(x) \cdot f(y)$, for all $x, y \in[0,1]$, and $f(0) \neq 0$. If $y=y(x)$ satisfies the differential...
JEE Main Mathematics Medium
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Q JEE MAIN 2020
The differential equation of the family of curves, $x^2=4 b(y+b), b \in R$, is
JEE Main Mathematics Easy
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Q JEE MAIN 2019
JEE Main Mathematics Medium
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Q JEE MAIN 2020
If $y=y(x)$ is the solution of the differential equation, $e^y\left(\frac{d y}{d x}-1\right)=e^x$ such that $y(0)=0$, then $y(1)$ is equal to
JEE Main Mathematics Easy
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Q JEE Main 2021
If $y \frac{d y}{d x}=x\left|\frac{y^2}{x^2}+\frac{\phi\left(\frac{y^2}{x^2}\right)}{\phi^{\prime}\left(\frac{y^2}{x^2}\right)}\right|, x>0, \phi>0$, and $y(1)=-1$, then $\phi\left(\frac{y^2}{4}\right)$ is equal to :
JEE Main Mathematics Hard
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Q JEE MAIN 2019
The curve amongst the family of curves represented by the differential equation, $\left(x^2-y^2\right) d x+2 x y d y=0$ which passes through $(1,1)$ is
JEE Main Mathematics Easy
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