Question:medium
If the curve \(y=f(x)\) passes through the point \((1,e)\) and satisfies the differential equation}
\[
dy=y(2+\log_e x)\,dx,\quad x>0,
\]
then \(f(e)\) is equal to:
If the curve \(y=f(x)\) passes through the point \((1,e)\) and satisfies the differential equation}
\[
dy=y(2+\log_e x)\,dx,\quad x>0,
\]
then \(f(e)\) is equal to:
Updated On: Apr 10, 2026
- \(e^{e}\)
- \(e^{e^2}\)
- \(e^{2e}\)
- \(e^{2e}\)
Show Solution
The Correct Option is A
Solution and Explanation
Was this answer helpful?
0
Top Questions on Differential Equations
- If for the solution curve \( y = f(x) \) of the differential equation \[ \frac{dy}{dx} + (\tan x) y = 2 + \sec^2 x, \quad y(\frac{\pi}{3}) = \sqrt{3}, \] \(\text{then}\) \( y(\frac{\pi}{4}) \) is equal to:
- JEE Main - 2025
- Mathematics
- Differential Equations
- If \( x = f(y) \) is the solution of the differential equation \[ (1 + y^2) + (x - 2e^{\tan^{-1}y}) \frac{dy}{dx} = 0, \quad y \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right), \] with \( f(0) = 1 \), then \( f\left( \frac{1}{\sqrt{3}} \right) \) is equal to:
- JEE Main - 2025
- Mathematics
- Differential Equations
Let \( y = f(x) \) be the solution of the differential equation\[\frac{dy}{dx} + \frac{xy}{x^2 - 1} = \frac{x^6 + 4x}{\sqrt{1 - x^2}}, \quad -1 < x < 1\] such that \( f(0) = 0 \). If \[6 \int_{-1/2}^{1/2} f(x)dx = 2\pi - \alpha\] then \( \alpha^2 \) is equal to ______.
- JEE Main - 2025
- Mathematics
- Differential Equations
If \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] and
and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to:
- JEE Main - 2025
- Mathematics
- Differential Equations
- Want to practice more? Try solving extra ecology questions todayView All Questions
