New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differential Equations question

2024 · 8 Apr · Shift 1 · Q36

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

PYQ Library
JEE Main
Mathematics
Differential Equations
2024 · 8 Apr · Shift 1 · Q36

Differential Equations question

2024 · 8 Apr · Shift 1 · Q36

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

f(x)

be a positive function such that the area bounded by

y=f(x), y=0

from

x=0

to

x=a\gt 0

is

e^{-a}+4 a^2+a-1

. Then the differential equation, whose general solution is

y=c_1 f(x)+c_2

, where

c_1

and

c_2

are arbitrary constants, is

A
$\left(8 e^x+1\right) \frac{d^2 y}{d x^2}-\frac{d y}{d x}=0$
B
$\left(8 e^x+1\right) \frac{d^2 y}{d x^2}+\frac{d y}{d x}=0$
C
$\left(8 e^x-1\right) \frac{d^2 y}{d x^2}-\frac{d y}{d x}=0$
D
$\left(8 e^x-1\right) \frac{d^2 y}{d x^2}+\frac{d y}{d x}=0$

More from Differential Equations

Let $y = y (x)$ be the solution of the differential equation $(1 + y^{2}) e^{t a n x} d x + cos^{2} x (1 + e^{2 t a n x}) d y = 0, y (0) = 1$ . Then $y (\frac{π}{4})$ is equal to2024 · MCQ
Let $y = y (x)$ be the solution curve of the differential equation $sec y \frac{d y}{d x} + 2 x sin y = x^{3} cos y, y (1) = 0$ . Then $y (3)$ is equal to:2024 · MCQ
Let $α ∣ x ∣ = ∣ y ∣ e^{x y - β}, α, β \in N$ be the solution of the differential equation $x d y - y d x + x y (x d y + y d x) = 0, y (1) = 2$ . Then $α + β$ is equal to …2024 · Numerical
The solution of the differential equation $(x^{2} + y^{2}) d x - 5 x y d y = 0, y (1) = 0$ , is :2024 · MCQ
The solution curve, of the differential equation $2 y \frac{d y}{d x} + 3 = 5 \frac{d y}{d x}$ , passing through the point $(0, 1)$ is a conic, whose vertex lies on the line :2024 · MCQ
Let $0 \int x 1 - (y^{'} (t))^{2} d t = \int_{0}^{x} y (t) d t, 0 \leq x \leq 3, y \geq 0, y (0) = 0$ . Then at $x = 2, y^{''} + y + 1$ is equal to2024 · MCQ
For a differentiable function $f : R \to R$ , suppose $f^{'} (x) = 3 f (x) + α$ , where $α \in R, f (0) = 1$ and $lim_{x \to - \infty} f (x) = 7$ . Then $9 f (- lo g_{e} 3)$ is equal…2024 · Numerical
Let $x = x (t)$ and $y = y (t)$ be solutions of the differential equations $\frac{d x}{dt} + a x = 0$ and $\frac{d y}{dt} + by = 0$ respectively, $a, b \in R$ …2024 · MCQ