Question:

Given that dy/dx = ye^x such that x = 0, y = e. The value of y(y > 0) when x = 1 will be

Updated On: Jul 30, 2024

Hide Solution

Verified By Collegedunia

The Correct Option is C

Solution and Explanation

The correct answer is option C) e^e

Given that dy/dx = ye^x
such that x = 0, y = e.
The value of y(y > 0) when x = 1 will be

dy/y = exdx

⇒ ln y = e^x + c

At x = 0, y = e.
So, c = 0. ln y = e^x

Therefore, at x = 1, y = e^e.

Was this answer helpful?

Top Questions on 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
View Solution
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
View Solution
Let $f(x)$ be a real differentiable function such that $f(0) = 1$ and $f(x + y) = f(x)f'(y) + f'(x)f(y)$ for all $x, y \in \mathbb{R}$ . Then $\sum_{n=1}^{100} \log_e f(n)$ is equal to :
- JEE Main - 2025
- Mathematics
- Differential equations
View Solution
Let $x = x(y)$ be the solution of the differential equation $y^2 dx + \left( x - \frac{1}{y} \right) dy = 0$ . If $x(1) = 1$ , then $x\left( \frac{1}{2} \right)$ is :
- JEE Main - 2025
- Mathematics
- Differential equations
View Solution
Let $f : \mathbb{R} \to \mathbb{R}$ be a twice differentiable function such that $f(x + y) = f(x) f(y)$ for all $x, y \in \mathbb{R}$ . If $f'(0) = 4a$ and $f$ satisfies $f''(x) - 3a f'(x) - f(x) = 0$ , where $a > 0$ , then the area of the region R = {(x, y) | 0 $\leq$ y $\leq$ f(ax), 0 $\leq$ x $\leq$ 2\ is :
- JEE Main - 2025
- Mathematics
- Differential equations
View Solution

View More Questions

Questions Asked in JEE Main exam