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Differential Equations

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2025
Let $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}+2 y \sec ^2 x=2 \sec ^2 x+3 \tan x \cdot \sec ^2 x$...
JEE Main Mathematics Easy
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Q JEE MAIN_2025
Let $y=y(x)$ be the solution of the differential equation $\left(x^2+1\right) y^2-2 x y=\left(x^4+2 x^2+1\right) \cos x$. $y(0)=1$. Then $\int_{-2}^3 y(x) \mathrm{d} x$ is:
JEE Main Physics Medium
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Q JEE MAIN 2025
If a curve $y=y(x)$ passes through the point $\left(1, \frac{\pi}{2}\right)$ and satisfies 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
$\frac{d y}{d x}+3\left(\tan ^2 x\right) y+3 y=\sec ^2 x, y(0)=\frac{1}{3}+e^3$. Then $y\left(\frac{\pi}{4}\right)$ is equal to
JEE Main Mathematics Easy
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Q JEE MAIN 2023
Let $y=y_1(x)$ and $y=y_2(x)$ be the solution curves of the differential equation $\frac{d y}{d x}=y+7$ with initial conditions $y_1(0)=y_2(0)=1$ respectively. Then the curves $y=y_1(x)$ and...
JEE Main Mathematics Easy
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Q JEE MAIN 2023
Let $x=x(y)$ be the solution of the differential equation $2(y+2) \log _e(y+2) d x+\left(x+4-2 \log _e(y+2)\right) d y=0, y>-1$ with $x\left(e^4-2\right)=1$. Then $x\left(e^9-2\right)$ is equal...
JEE Main Mathematics Medium
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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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