New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2023 · 6 Apr · Shift 2 · Q30

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

PYQ Library
JEE Main
Mathematics
Differential Equations
2023 · 6 Apr · Shift 2 · Q30

Differential Equations question

2023 · 6 Apr · Shift 2 · Q30

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

If the solution curve

f(x, y)=0

of the differential equation

\left(1+\log _{e} x\right) \frac{d x}{d y}-x \log _{e} x=e^{y}, x \gt 0

, passes through the points

(1,0)

and

(\alpha, 2)

, then

\alpha^{\alpha}

is equal to :

A
$e^{\sqrt{2} e^{2}}$
B
$e^{2 e^{\sqrt{2}}}$
C
$e^{e^{2}}$
D
$e^{2 e^{2}}$

More from Differential Equations

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
Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} + \frac{5}{x ( x ^{5} + 1 )} y = \frac{( x ^{5} + 1 ) ^{2}}{x ^{7}}, x > 0$ . If $y (1) = 2$ , then $y (2)$ is equal to :2023 · MCQ
Let $y = y (x), y > 0$ , be a solution curve of the differential equation $(1 + x^{2}) d y = y (x - y) d x$ . If $y (0) = 1$ and $y (22) = β$ , then2023 · MCQ
Let $y = y_{1} (x)$ and $y = y_{2} (x)$ be the solution curves of the differential equation $\frac{d y}{d x} = y + 7$ with initial conditions $y_{1} (0) = 0$ and $y_{2} (0) = 1$ respectively. Then the curves $y = y_{1} (x)$ and $y = y_{2} (x)$ intersect at2023 · MCQ