New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2025 · 3 Apr · Shift 1 · Q39

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Differential Equations
2025 · 3 Apr · Shift 1 · Q39

Differential Equations question

2025 · 3 Apr · Shift 1 · Q39

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

g

be a differentiable function such that

\int_0^x g(t) d t=x-\int_0^x \operatorname{tg}(t) d t, x \geq 0

and let

y=y(x)

satisfy the differential equation

\frac{d y}{d x}-y \tan x=2(x+1) \sec x g(x), x \in\left[0, \frac{\pi}{2}\right)

. If

y(0)=0

, then

y\left(\frac{\pi}{3}\right)

is equal to

A
$\frac{4 \pi}{3}$
B
$\frac{2 \pi}{3}$
C
$\frac{2 \pi}{3 \sqrt{3}}$
D
$\frac{4 \pi}{3 \sqrt{3}}$

More from Differential Equations

Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} + 3 (tan^{2} x) y + 3 y = sec^{2} x, y (0) = \frac{1}{3} + e^{3}$ . Then $y (\frac{π}{4})$ is equal to :2025 · MCQ
If a curve $y = y (x)$ passes through the point $(1, \frac{π}{2})$ and satisfies the differential equation $(7 x^{4} cot y - e^{x} cosec y) \frac{d x}{d y} = x^{5}, x \geq 1$ , then at $x = 2$ …2025 · MCQ
Let $y = y (x)$ be the solution curve of the differential equation $x (x^{2} + e^{x}) d y + (e^{x} (x - 2) y - x^{3}) d x = 0, x > 0$ , passing through the point $y (2)$ . Then $y (2)$ is equal to :2025 · MCQ
Let y = y(x) be the solution of the differential equation $(x^{2} + 1) y^{'} - 2 x y = (x^{4} + 2 x^{2} + 1) cos x$ , $y (0) = 1$ . Then $- 3 \int 3 y (x) d x$ is :2025 · MCQ
Let $f (x) = x - 1$ and $g (x) = e^{x}$ for $x \in R$ . If $\frac{d y}{d x} = (e^{- 2 x} g (f (f (x))) - \frac{y}{x})$ , $y (0) = 0$ , then $y (1)$ is2025 · MCQ
Let $x = x (y)$ be the solution of the differential equation $y^{2} d x + (x - \frac{1}{y}) d y = 0$ . If $x (1) = 1$ , then $x (\frac{1}{2})$ is :2025 · MCQ
Let $f (x)$ be a real differentiable function such that $f (0) = 1$ and $f (x + y) = f (x) f^{'} (y) + f^{'} (x) f (y)$ for all $x, y \in R$ . Then $\sum_{n = 1}^{100} lo g_{e} f (n)$ is equal to :2025 · MCQ
Let $f : R \to R$ be a twice differentiable function such that $f (x + y) = f (x) f (y)$ for all $x, y \in R$ . If $f^{'} (0) = 4 a$ and $f$ satisfies $f^{''} (x) - 3 a f^{'} (x) - f (x) = 0, a > 0$ …2025 · MCQ