New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2022 · 26 Jun · Shift 1 · Q41

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

PYQ Library
JEE Main
Mathematics
Differential Equations
2022 · 26 Jun · Shift 1 · Q41

Differential Equations question

2022 · 26 Jun · Shift 1 · Q41

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

Let

S = (0,2\pi ) - \left\{ {{\pi \over 2},{{3\pi } \over 4},{{3\pi } \over 2},{{7\pi } \over 4}} \right\}

. Let

y = y(x)

, x

\in

S, be the solution curve of the differential equation

{{dy} \over {dx}} = {1 \over {1 + \sin 2x}},\,y\left( {{\pi \over 4}} \right) = {1 \over 2}

. If the sum of abscissas of all the points of intersection of the curve y = y(x) with the curve

y = \sqrt 2 \sin x

is

{{k\pi } \over {12}}

, then k is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Differential Equations

If $y = y (x)$ is the solution of the differential equation $x \frac{d y}{d x} + 2 y = x e^{x}$ , $y (1) = 0$ then the local maximum value of the function $z (x) = x^{2} y (x) - e^{x}, x \in R$ is :2022 · MCQ
If the solution of the differential equation $\frac{d y}{d x} + e^{x} (x^{2} - 2) y = (x^{2} - 2 x) (x^{2} - 2) e^{2 x}$ satisfies $y (0) = 0$ , then the value of y(2) is…2022 · MCQ
Let $y = y_{1} (x)$ and $y = y_{2} (x)$ be two distinct solutions of the differential equation $\frac{d y}{d x} = x + y$ , with $y_{1} (0) = 0$ and $y_{2} (0) = 1$ respectively. Then, the number of points of intersection of $y = y_{1} (x)$ and $y = y_{2} (x)$ is2022 · MCQ
Let $y = y (x)$ be the solution curve of the differential equation $sin (2 x^{2}) lo g_{e} (tan x^{2}) d y + (4 x y - 42 x sin (x^{2} - \frac{π}{4})) d x = 0$ , $0 < x < \frac{π}{2}$ …2022 · Numerical
If $\frac{d y}{d x} + \frac{2 ^{x - y} ( 2 ^{y} - 1 )}{2 ^{x} - 1} = 0$ , x, y > 0, y(1) = 1, then y(2) is equal to :2022 · MCQ
If the solution curve of the differential equation $((tan^{- 1} y) - x) d y = (1 + y^{2}) d x$ passes through the point (1, 0), then the abscissa of the point on the curve whose ordinate is tan(1), is2022 · MCQ
Let $y = y (x)$ be the solution of the differential equation $(1 - x^{2}) d y = (x y + (x^{3} + 2) 1 - x^{2}) d x, - 1$ -$$1 is equal to $\underline{\hspace{2cm}}$.2022 · Numerical
Let the solution curve of the differential equation $x d y = (x^{2} + y^{2} + y) d x, x > 0$ , intersect the line $x = 1$ at $y = 0$ and the line $x = 2$ at $y = α$ . Then the value of $α$ is :2022 · MCQ