New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2022 · 28 Jun · Shift 2 · Q32

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

PYQ Library
JEE Main
Mathematics
Differential Equations
2022 · 28 Jun · Shift 2 · Q32

Differential Equations question

2022 · 28 Jun · Shift 2 · Q32

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2

\tan x(\cos x - y)

. If the curve passes through the point

\left( {{\pi \over 4},0} \right)

, then the value of

\int\limits_0^{\pi /2} {y\,dx}

is equal to :

A
$(2 - \sqrt 2 ) + {\pi \over {\sqrt 2 }}$
B
$2 - {\pi \over {\sqrt 2 }}$
C
$(2 + \sqrt 2 ) + {\pi \over {\sqrt 2 }}$
D
$2 + {\pi \over {\sqrt 2 }}$

More from Differential Equations

Let the solution curve $y = y (x)$ of the differential equation $(1 + e^{2 x}) (\frac{d y}{d x} + y) = 1$ pass through the point $(0, \frac{π}{2})$ . Then, $x \to \infty lim e^{x} y (x)$ …2022 · MCQ
If the solution curve of the differential equation $\frac{d y}{d x} = \frac{x + y - 2}{x - y}$ passes through the points $(k + 1, 2), k > 0$ and $(k + 1, 2), k > 0$ , then2022 · MCQ
Let $y = y (x)$ be the solution curve of the differential equation $\frac{d y}{d x} + (\frac{2 x ^{2} + 11 x + 13}{x ^{3} + 6 x ^{2} + 11 x + 6}) y = \frac{( x + 3 )}{x + 1}, x > - 1$ , which passes through the point $y (1)$ . Then $y (1)$ is equal to :2022 · MCQ
Let the solution curve of the differential equation $x \frac{d y}{d x} - y = y^{2} + 16 x^{2}$ , $y (1) = 3$ be $y = y (x)$ . Then y(2) is equal to:2022 · MCQ
Let y = y(x) be the solution of the differential equation $${{dy} \over {dx}} + {{\sqrt 2 y} \over {2{{\cos }^4}x - {{\cos }^2}x}} = x{e^{{{\tan }^{ - 1}}(\sqrt 2 \cot 2x)}},\,0 2 is equal to $\underline{\hspace{2cm}}$.2022 · Numerical
If y = y(x) is the solution of the differential equation $(1 + e^{2 x}) \frac{d y}{d x} + 2 (1 + y^{2}) e^{x} = 0$ and y (0) = 0, then $6 (y^{'} (0) + (y (lo g_{e} 3))^{2})$ …2022 · MCQ
Let y = y(x), x > 1, be the solution of the differential equation $(x - 1) \frac{d y}{d x} + 2 x y = \frac{1}{x - 1}$ , with $y (2) = \frac{1 + e ^{4}}{2 e ^{4}}$ . If $y (3) = \frac{e ^{α} + 1}{β e ^{α}}$ , then the…2022 · Numerical
If y = y(x) is the solution curve of the differential equation $x^{2} d y + (y - \frac{1}{x}) d x = 0$ ; x > 0 and y(1) = 1, then $y (\frac{1}{2})$ is equal to :2021 · MCQ