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Differential Equations

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2025
Let g be a differentiable function such that $\int_0^x g (t)dt = x - \int_0^x t g(t)dt,x \ge 0$ and let $y = y(x)$ satisfy...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Let $f:R \to R$ be a thrice differentiable odd function satisfying ${f^\prime }(x) \ge 0,{f^{\prime \prime }}(x) = f(x),f(0) = 0,{f^\prime }(0) = 3$. Then...
JEE Main Mathematics Hard
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Q JEE MAIN 2025
Let $y=y(x)$ be the solution of the differential equation $2 \cos x \frac{\mathrm{~d} y}{\mathrm{~d} x}=\sin 2 x-4 y \sin x, x \in\left(0, \frac{\pi}{2}\right)$. If $y\left(\frac{\pi}{3}\right)=0$,...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let $x=x(y)$ be the solution of the differential equation $y=\left(x-y \frac{d x}{d y}\right) \sin \left(\frac{x}{y}\right), y>0$ and $x(1)=\frac{\pi}{2}$
Then $\cos (x(2))$ is equal to...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Let $y = y(x)$ be the solution of the differential equation $...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Let y = y(x) be the solution of the differential equation $...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let a curve $y = f(x)$ pass through the points (0,5) and $\left( {{{\log }_e}2,k} \right)$. If the curve satisfies the differential equation $...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
If $x=f(y)$ is the solution of the differential equation $$ \left(1+y^2\right)+\left(x-2 \mathrm{e}^{\tan ^{-1} y}\right) \frac{\mathrm{d} y}{\mathrm{~d} x}=0, y \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) $$ with $f(0)=1$, then $f\left(\frac{1}{\sqrt{3}}\right)$...
JEE Main Mathematics Easy
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