EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 27 August 2021 Shift 1>Q 3

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JEE Main

IMPORTANT

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Let us consider a curve, $y = f (x)$ passing through the point $(- 2, 2)$ and the slope of the tangent to the curve at any point $(x, f (x))$ is given by $f (x) + x f^{'} (x) = x^{2} .$ Then

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Important Questions on Differential Equations

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 27 August 2021 Shift 1>Q 4

Let

y = y (x)

be the solution of the differential equation

\frac{d y}{d x} = 2 (y + 2 \sin x - 5) x - 2 \cos x

such that

y (0) = 7 .

Then

y (π)

is equal to

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 27 August 2021 Shift 1>Q 5

If

y^{1 / 4} + y^{- 1 / 4} = 2 x,

and

(x^{2} - 1) \frac{d^{2} y}{d x^{2}} + α x \frac{d y}{d x} + β y = 0,

then

| α - β |

is equal to _______.

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 27 August 2021 Shift 2>Q 6

If the solution curve of the differential equation

(2 x - 10 y^{3}) d y + y d x = 0

, passes through the points

(0, 1)

and

(2, β)

, then

β

is a root of the equation?

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 27 August 2021 Shift 2>Q 7

A differential equation representing the family of parabolas with axis parallel to

y -

axis and whose length of latus rectum is the distance of the point

(2, - 3)

from the line

3 x + 4 y = 5

, is given by:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 31 August 2021 Shift 1>Q 8

If

\frac{d y}{d x} = \frac{2^{x + y} - 2^{x}}{2^{y}}, y (0) = 1,

then

y (1)

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 31 August 2021 Shift 1>Q 9

If

x ϕ (x) = \int_{5}^{x} (3 t^{2} - 2 ϕ^{'} (t)) d t, x > - 2,

ϕ (0) = 4,

then

ϕ (2)

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 31 August 2021 Shift 2>Q 10

If

y \frac{d y}{d x} = x [\frac{y^{2}}{x^{2}} + \frac{ϕ (\frac{y^{2}}{x^{2}})}{ϕ^{'} (\frac{y^{2}}{x^{2}})}], x > 0, ϕ > 0,

and

y (1) = - 1,

then

ϕ (\frac{y^{2}}{4})

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 31 August 2021 Shift 2>Q 11

If

\frac{d y}{d x} = \frac{2^{x} y + 2^{y} \cdot 2^{x}}{2^{x} + 2^{x + y} \log_{e} 2}, y (0) = 0,

then for

y = 1,

the value of

x

lies in the interval :