New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2024 · 27 Jan · Shift 2 · Q42

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

PYQ Library
JEE Main
Mathematics
Differential Equations
2024 · 27 Jan · Shift 2 · Q42

Differential Equations question

2024 · 27 Jan · Shift 2 · Q42

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

If

y=y(x)

is the solution curve of the differential equation

\left(x^2-4\right) \mathrm{d} y-\left(y^2-3 y\right) \mathrm{d} x=0, x\gt 2, y(4)=\frac{3}{2}

and the slope of the curve is never zero, then the value of

y(10)

equals :

A
$\frac{3}{1+(8)^{1 / 4}}$
B
$\frac{3}{1-(8)^{1 / 4}}$
C
$\frac{3}{1-2 \sqrt{2}}$
D
$\frac{3}{1+2 \sqrt{2}}$

More from Differential Equations

If the solution curve, of the differential equation $\frac{d y}{d x} = \frac{x + y - 2}{x - y}$ passing through the point $tan^{- 1} (\frac{y - 1}{x - 1}) - \frac{1}{β} lo g_{e} (α + (\frac{y - 1}{x - 1})^{2}) = lo g_{e} ∣ x - 1∣$ is $tan^{- 1} (\frac{y - 1}{x - 1}) - \frac{1}{β} lo g_{e} (α + (\frac{y - 1}{x - 1})^{2}) = lo g_{e} ∣ x - 1∣$ …2024 · Numerical
A function $y = f (x)$ satisfies $f (x) sin 2 x + sin x - (1 + cos^{2} x) f^{'} (x) = 0$ with condition $f (0) = 0$ . Then, $f (\frac{π}{2})$ is equal to2024 · MCQ
If the solution curve $y = y (x)$ of the differential equation $(1 + y^{2}) (1 + lo g_{e} x) d x + x d y = 0, x > 0$ passes through the point $y (e) = \frac{α - t a n ( \frac{3}{2} )}{β + t a n ( \frac{3}{2} )}$ and $y (e) = \frac{α - t a n ( \frac{3}{2} )}{β + t a n ( \frac{3}{2} )}$ …2024 · Numerical
If $sin (\frac{y}{x}) = lo g_{e} ∣ x ∣ + \frac{α}{2}$ is the solution of the differential equation $x cos (\frac{y}{x}) \frac{d y}{d x} = y cos (\frac{y}{x}) + x$ and $y (1) = \frac{π}{3}$ , then $α^{2}$ …2024 · MCQ
Let $y = y (x)$ be the solution of the differential equation $sec x d y + {2 (1 - x) tan x + x (2 - x)} d x = 0$ such that $y (0) = 2$ . Then $y (2)$ is equal to:2024 · MCQ
Let $y = y (x)$ be the solution of the differential equation $(1 - x^{2}) d y = [x y + (x^{3} + 2) 3 (1 - x^{2})] d x, - 1 < x < 1, y (0) = 0$ . If $y (\frac{1}{2}) = \frac{m}{n}, m$ …2024 · Numerical
Let $Y = Y (X)$ be a curve lying in the first quadrant such that the area enclosed by the line $Y - y = Y^{'} (x) (X - x)$ and the co-ordinate axes, where $\frac{- y ^{2}}{2 Y ^{'} ( x )} + 1, Y^{'} (x) e q 0$ is any point on the curve, is always $\frac{- y ^{2}}{2 Y ^{'} ( x )} + 1, Y^{'} (x) e q 0$ …2024 · Numerical
Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} = \frac{( t a n x ) + y}{s i n x ( s e c x - s i n x t a n x )}, x \in (0, \frac{π}{2})$ satisfying the condition $y (\frac{π}{4}) = 2$ . Then, $y (\frac{π}{3})$ …2024 · MCQ