New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2023 · 1 Feb · Shift 1 · Q34

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

PYQ Library
JEE Main
Mathematics
Differential Equations
2023 · 1 Feb · Shift 1 · Q34

Differential Equations question

2023 · 1 Feb · Shift 1 · Q34

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

If

y=y(x)

is the solution curve of the differential equation

\frac{d y}{d x}+y \tan x=x \sec x, 0 \leq x \leq \frac{\pi}{3}, y(0)=1

, then

y\left(\frac{\pi}{6}\right)

is equal to

A
$\frac{\pi}{12}-\frac{\sqrt{3}}{2} \log _{e}\left(\frac{2 \sqrt{3}}{e}\right)$
B
$\frac{\pi}{12}+\frac{\sqrt{3}}{2} \log _{e}\left(\frac{2 \sqrt{3}}{e}\right)$
C
$\frac{\pi}{12}+\frac{\sqrt{3}}{2} \log _{e}\left(\frac{2}{e \sqrt{3}}\right)$
D
$\frac{\pi}{12}-\frac{\sqrt{3}}{2} \log _{e}\left(\frac{2}{e \sqrt{3}}\right)$

More from Differential Equations

Let $α x = exp (x^{β} y^{γ})$ be the solution of the differential equation $2 x^{2} y d y - (1 - x y^{2}) d x = 0, x > 0, y (2) = lo g_{e} 2$ . Then $α + β - γ$ equals :2023 · MCQ
Let $y = y (x)$ be a solution of the differential equation $(x cos x) d y + (x y sin x + y cos x - 1) d x = 0, 0 < x < \frac{π}{2}$ . If $\frac{π}{3} y (\frac{π}{3}) = 3$ , then $\frac{π}{6} y^{''} (\frac{π}{6}) + 2 y^{'} (\frac{π}{6})$ …2023 · Numerical
If the solution curve $f (x, y) = 0$ of the differential equation $(1 + lo g_{e} x) \frac{d x}{d y} - x lo g_{e} x = e^{y}, x > 0$ , passes through the points $(α, 2)$ and $α^{α}$ , then $α^{α}$ is equal to :2023 · MCQ
If the solution curve of the differential equation $(y - 2 lo g_{e} x) d x + (x lo g_{e} x^{2}) d y = 0, x > 1$ passes through the points $(e, \frac{4}{3})$ and $(e^{4}, α)$ , then $α$ …2023 · Numerical
Let the solution curve $x = x (y), 0 < y < \frac{π}{2}$ , of the differential equation $(lo g_{e} (cos y))^{2} cos y d x - (1 + 3 x lo g_{e} (cos y)) sin y d y = 0$ satisfy $x (\frac{π}{3}) = \frac{1}{2 l o g _{e} 2}$ …2023 · Numerical
Let $f$ be a differentiable function such that $x^{2} f (x) - x = 4 0 \int x t f (t) d t$ , $f (1) = \frac{2}{3}$ . Then $18 f (3)$ is equal to :2023 · MCQ
Let the tangent at any point P on a curve passing through the points (1, 1) and $(\frac{1}{10}, 100)$ , intersect positive $x$ -axis and $y$ -axis at the points A and B respectively. If $PA : PB = 1 : k$ and…2023 · Numerical
Let $y = y (x)$ be a solution curve of the differential equation. $(1 - x^{2} y^{2}) d x = y d x + x d y$ . If the line $x = 1$ intersects the curve $y = y (x)$ at $y = 2$ and the line $x = 2$ intersects the curve $y = y (x)$ at $y = α$ , then a…2023 · MCQ