New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2025 · 8 Apr · Shift 2 · Q27

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

PYQ Library
JEE Main
Mathematics
Differential Equations
2025 · 8 Apr · Shift 2 · Q27

Differential Equations question

2025 · 8 Apr · Shift 2 · Q27

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

f(x) = x - 1

and

g(x) = e^x

for

x \in \mathbb{R}

. If

\frac{dy}{dx} = \left( e^{-2\sqrt{x}} g\left(f(f(x))\right) - \frac{y}{\sqrt{x}} \right)

,

y(0) = 0

, then

y(1)

is

A
$\frac{1 - e^3}{e^4}$
B
$\frac{e-1}{e^4}$
C
$\frac{1 - e^2}{e^4}$
D
$\frac{2e - 1}{e^3}$

More from Differential Equations

Let $x = x (y)$ be the solution of the differential equation $y^{2} d x + (x - \frac{1}{y}) d y = 0$ . If $x (1) = 1$ , then $x (\frac{1}{2})$ is :2025 · MCQ
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 $x, y \in R$ . Then $\sum_{n = 1}^{100} lo g_{e} f (n)$ is equal to :2025 · MCQ
Let $f : R \to R$ be a twice differentiable function such that $f (x + y) = f (x) f (y)$ for all $x, y \in R$ . If $f^{'} (0) = 4 a$ and $f$ satisfies $f^{''} (x) - 3 a f^{'} (x) - f (x) = 0, a > 0$ …2025 · MCQ
If $x = f (y)$ is the solution of the differential equation $(1 + y^{2}) + (x - 2 e^{t a n^{- 1} y}) \frac{d y}{d x} = 0, y \in (- \frac{π}{2}, \frac{π}{2})$ with $f (0) = 1$ , then $f (\frac{1}{3})$ …2025 · MCQ
Let $y = f (x)$ be the solution of the differential equation $\frac{d y}{d x} + \frac{x y}{x ^{2} - 1} = \frac{x ^{6} + 4 x}{1 - x ^{2}}, - 1 < x < 1$ such that $f (0) = 0$ . If $6 \int_{- 1/2}^{1/2} f (x) d x = 2 π - α$ then…2025 · Numerical
Let a curve $y = f (x)$ pass through the points $(lo g_{e} 2, k)$ and $(lo g_{e} 2, k)$ . If the curve satisfies the differential equation $2 (3 + y) e^{2 x} d x - (7 + e^{2 x}) d y = 0$ , then $k$ is equal to2025 · MCQ
Let $x = x (y)$ be the solution of the differential equation $y = (x - y \frac{d x}{d y}) sin (\frac{x}{y}), y > 0$ and $x (1) = \frac{π}{2}$ . Then $cos (x (2))$ is equal to :2025 · MCQ
Let $y = y (x)$ be the solution of the differential equation $(x y - 5 x^{2} 1 + x^{2}) d x + (1 + x^{2}) d y = 0, y (0) = 0$ . Then $y (3)$ is equal to2025 · MCQ