Differential Equations PYQs - Last 10 Years
JEE Advanced / Mathematics / Calculus / 13 recent questions
MathematicsCalculus2017-2026
Practice 13 JEE Advanced Mathematics questions from Differential Equations. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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Mathematics / Calculus
2017-2026
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MCQ30.8%
MCQM30.8%
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9 in last 5 years13 in last 10 years
Last 10 Years Differential Equations Questions
Showing 13 of 13 filtered questions.
1Differential Equations
Let $y = f(x)$ be the real valued function defined on the interval $(0, \infty)$, satisfying $y(1) = 0$ and the differential equation\(x \frac{dy}{dx} = y - x^3.\)Then which of the following statements is (are) TRUE?
MCQM+4 / -12026
2Differential Equations
Let $y : (-\infty, \infty) \to (0, \infty)$ be the solution of the differential equation
\(\frac{dy}{dx} = \frac{e^{5x} y^3 + y^3}{e^x + e^x y^4},\)
satisfying $y(0) = \frac{1}{\sqrt{2}}$. Then the value of $y(\log_e 2)$ is
\(\frac{dy}{dx} = \frac{e^{5x} y^3 + y^3}{e^x + e^x y^4},\)
satisfying $y(0) = \frac{1}{\sqrt{2}}$. Then the value of $y(\log_e 2)$ is
MCQ+3 / -12026
3Differential Equations
Let $y(x)$ be the solution of the differential equation
\(x^2 \frac{d y}{d x}+x y=x^2+y^2, \quad x>\frac{1}{e}\)
satisfying $y(1)=0$. Then the value of $2 \frac{(y(e))^2}{y\left(e^2\right)}$ is ____________.
\(x^2 \frac{d y}{d x}+x y=x^2+y^2, \quad x>\frac{1}{e}\)
satisfying $y(1)=0$. Then the value of $2 \frac{(y(e))^2}{y\left(e^2\right)}$ is ____________.
INTEGER+4 / -02025
4Differential Equations
For all x > 0, let y₁(x), y₂(x), and y₃(x) be the functions satisfying
$ \frac{dy_1}{dx} - (\sin x)^2 y_1 = 0, \quad y_1(1) = 5, $ $ \frac{dy_2}{dx} - (\cos x)^2 y_2 = 0, \quad y_2(1) = \frac{1}{3}, $ $ \frac{dy_3}{dx} - \frac{(2-x^3)}{x^3}...
$ \frac{dy_1}{dx} - (\sin x)^2 y_1 = 0, \quad y_1(1) = 5, $ $ \frac{dy_2}{dx} - (\cos x)^2 y_2 = 0, \quad y_2(1) = \frac{1}{3}, $ $ \frac{dy_3}{dx} - \frac{(2-x^3)}{x^3}...
INTEGER+4 / -02025
5Differential Equations
Let $f(x)$ be a continuously differentiable function on the interval $(0, \infty)$ such that $f(1)=2$ and
\(\lim\limits_{t \rightarrow x} \frac{t^{10} f(x)-x^{10} f(t)}{t^9-x^9}=1\)
for each $x>0$. Then, for all $x>0, f(x)$ is equal to ...
\(\lim\limits_{t \rightarrow x} \frac{t^{10} f(x)-x^{10} f(t)}{t^9-x^9}=1\)
for each $x>0$. Then, for all $x>0, f(x)$ is equal to ...
MCQ+3 / -12024
6Differential Equations
For $x \in \mathbb{R}$, let $y(x)$ be a solution of the differential equation
$\left(x^2-5\right) \frac{d y}{d x}-2 x y=-2 x\left(x^2-5\right)^2$ such that $y(2)=7$.
Then the maximum value of the function $y(x)$ is :
$\left(x^2-5\right) \frac{d y}{d x}-2 x y=-2 x\left(x^2-5\right)^2$ such that $y(2)=7$.
Then the maximum value of the function $y(x)$ is :
INTEGER+4 / -02023
7Differential Equations
Let $f:[1, \infty) \rightarrow \mathbb{R}$ be a differentiable function such that $f(1)=\frac{1}{3}$ and $3 \int\limits_1^x f(t) d t=x f(x)-\frac{x^3}{3}, x \in[1, \infty)$. Let $e$ denote the base of the natural logarithm. Then the value o...
MCQ+3 / -12023
8Differential Equations
For $x \in \mathbb{R}$, let the function $y(x)$ be the solution of the differential equation
\(\frac{d y}{d x}+12 y=\cos \left(\frac{\pi}{12} x\right), \quad y(0)=0\)
Then, which of the following statements is/are TRUE ?
\(\frac{d y}{d x}+12 y=\cos \left(\frac{\pi}{12} x\right), \quad y(0)=0\)
Then, which of the following statements is/are TRUE ?
MCQM+4 / -22022
9Differential Equations
If $y(x)$ is the solution of the differential equation
\(x d y-\left(y^{2}-4 y\right) d x=0 \text { for } x > 0, y(1)=2,\)
and the slope of the curve $y=y(x)$ is never zero, then the value of $10 y(\sqrt{2})$ is
\(x d y-\left(y^{2}-4 y\right) d x=0 \text { for } x > 0, y(1)=2,\)
and the slope of the curve $y=y(x)$ is never zero, then the value of $10 y(\sqrt{2})$ is
INTEGER+3 / -12022
10Differential Equations
Let \(\Gamma\) denote a curve y = y(x) which is in the first quadrant and let the point (1, 0) lie on it. Let the tangent to I` at a point P intersect the y-axis at YP. If PYP has length 1 for each point P on I`, then which of the followin...
MCQM+4 / -12019
11Differential Equations
Let f : R \(\to\) R be a differentiable function with f(0) = 0. If y = f(x) satisfies the differential equation \({{dy} \over {dx}} = (2 + 5y)(5y - 2)\), then the value of \(\mathop {\lim }\limits_{n \to - \infty } f(x)\) is ...........
INTEGER+3 / -02018
12Differential Equations
If \(g(x) = \int_{\sin x}^{\sin (2x)} {{{\sin }^{ - 1}}} (t)\,dt\), then
MCQM+4 / -22017
13Differential Equations
If y = y(x) satisfies the differential equation\({8\sqrt x \left( {\sqrt {9 + \sqrt x } } \right)dy = {{\left( {\sqrt {4 + \sqrt {9 + \sqrt x } } } \right)}^{ - 1}}}\)dx, x > 0 and y(0) = \(\sqrt 7\), then y(256) =
MCQ+3 / -12017