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Differential Equations

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2026
Let $y=y(x)$ be the solution of the differential equation $$ x \frac{d y}{d x}-\sin 2 y=x^3\left(2-x^3\right) \cos ^2 y, x \neq 0 . $$ If...
JEE Main Mathematics Medium
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Q JEE MAIN 2026
If the solution curve $y=f(x)$ of the differential equation $$ \left(x^2-4\right) y^{\prime}-2 x y+2 x\left(4-x^2\right)^2=0, x>2, $$
passes through the point $(3,15)$, then the local...
JEE Main Mathematics Easy
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Q JEE MAIN 2026
Let a differentiable function f satisfy the equation $\int_0^{36} f\left(\frac{t x}{36}\right) d t=4 \alpha f(x)$. If $y=f(x)$ is a standard parabola passing through the points...
JEE Main Mathematics Easy
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Q JEE MAIN_2026_
Let $y=y(x)$ be the solution of the differential equation $x^4 \mathrm{~d} y+\left(4 x^3 y+2 \sin x\right) \mathrm{d} x=0$, $x>0, y\left(\frac{\pi}{2}\right)=0$. Then $\pi^4 y\left(\frac{\pi}{3}\right)$ is equal...
JEE Main Mathematics Medium
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Q JEE MAIN 2026
If $y=y(x)$ satisfies the differential equation $16(\sqrt{x+9 \sqrt{x}})(4+\sqrt{9+\sqrt{x}}) \cos y \mathrm{~d} y=(1+2 \sin y) \mathrm{d} x, x>0$ and $y(256)=\frac{\pi}{2}, y(49)=\alpha$, then $2 \sin \alpha$ is...
JEE Main Mathematics Hard
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Q JEE MAIN_2026_
Let the solution curve of the differential equation $x d y-y d x=\sqrt{x^2+y^2} d x, x>0, y(1)=0$, be $y=y(x)$. Then $y(3)$ is equal to
JEE Main Mathematics Medium
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Q JEE MAIN 2026
Let $y=y(x)$ be the solution of the differential equation $\sec x \frac{\mathrm{~d} y}{\mathrm{~d} x}-2 y=2+3 \sin x, x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right), y(0)=-\frac{7}{4}$. Then $y\left(\frac{\pi}{6}\right)$ is equal...
JEE Main Mathematics Easy
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Q JEE MAIN 2026
Let $y=y(x)$ be the solution curve of the differential equation $\left(1+x^2\right) d y+\left(y-\tan ^{-1} x\right) d x=0, y(0)=1$. Then the value of $y(1)$ is :
JEE Main Mathematics Easy
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Q JEE MAIN_2019_
If $y=y(x)$ is the solution of the differential equation $\frac{\mathrm{dt}}{\mathrm{dx}}=(\tan \mathrm{x}-\mathrm{y}) \sec ^2 \mathrm{x}, \mathrm{x} \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, such that $\mathrm{y}(0) =0$, then $\mathrm{y}\left(-\frac{\pi}{4}\right)$ is equal...
JEE Main Mathematics Medium
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Q JEE MAIN 2019
The solution of the differential equation $x \frac{d y}{d x}+2 y=x^2(x \neq 0)$ with $y(1)=1$, is :
JEE Main Mathematics Easy
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