New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2023 · 8 Apr · Shift 1 · Q41

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

PYQ Library
JEE Main
Mathematics
Differential Equations
2023 · 8 Apr · Shift 1 · Q41

Differential Equations question

2023 · 8 Apr · Shift 1 · Q41

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

If the solution curve of the differential equation

\left(y-2 \log _{e} x\right) d x+\left(x \log _{e} x^{2}\right) d y=0, x \gt 1

passes through the points

\left(e, \frac{4}{3}\right)

and

\left(e^{4}, \alpha\right)

, then

\alpha

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Differential Equations

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
If $y = y (x)$ is the solution of the differential equation $\frac{d y}{d x} + \frac{4 x}{( x ^{2} - 1 )} y = \frac{x + 2}{( x ^{2} - 1 ) ^{\frac{5}{2}}}, x > 1$ such that $y (2) = \frac{2}{9} lo g_{e} (2 + 3) and y (2) = α lo g_{e} (α + β) + β - γ, α, β, γ \in N, then α β γ is equal to$ …2023 · Numerical