EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 25 June 2022 Shift 1>Q 95

HARD

JEE Main

IMPORTANT

Earn 100

Let $y = y (x)$ be the solution of the differential equation $(x + 1) y^{'} - y = e^{3 x} {(x + 1)}^{2}$ , with $y (0) = \frac{1}{3}$ . Then, the point $x = - \frac{4}{3}$ for the curve $y = y (x)$ is

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Important Questions on Differential Equations

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 25 June 2022 Shift 1>Q 96

If the solution curve

y = y (x)

of the differential equation

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

, which passes through the point

(1, 1)

and intersects the line

y = \sqrt{3} x

at the point

(α, \sqrt{3} α)

, then value of

\log_{e} (\sqrt{3} α)

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 25 June 2022 Shift 2>Q 97

If

y = y (x)

is the solution of the differential equation

2 x^{2} \frac{d y}{d x} - 2 x y + 3 y^{2} = 0

such that

y (e) = \frac{e}{3}

, then

y (1)

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 26 June 2022 Shift 2>Q 98

If

y = y (x)

is the solution of the differential equation

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

then the local maximum value of the function

z (x) = x^{2} y (x) - e^{x}, x \in R

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 26 June 2022 Shift 2>Q 99

If

\frac{d y}{d x} + e^{x} (x^{2} - 2) y = (x^{2} - 2 x) (x^{2} - 2) e^{2 x}

and

y (0) = 0

, then the value of

y (2)

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 26 June 2022 Shift 1>Q 100

Let the solution curve

y = y (x)

of the differential equation

(4 + x^{2}) d y - 2 x (x^{2} + 3 y + 4) d x = 0

pass through the origin. Then

y (2)

is equal to _____.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 26 June 2022 Shift 1>Q 101

Let

S = (0, 2 π) - \{\frac{π}{2}, \frac{3 π}{4}, \frac{3 π}{2}, \frac{7 π}{4}\}

. Let

y = y (x)

,

x \in S

, be the solution curve of the differential equation

\frac{d y}{d x} = \frac{1}{1 + \sin 2 x}, y (\frac{π}{4}) = \frac{1}{2}

. If the sum of abscissas of all the points of intersection of the curve

y = y (x)

with the curve

y = \sqrt{2} \sin x

is

\frac{k π}{12}

, then

k

is equal to _____.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 27 June 2022 Shift 1>Q 102

If

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

, then

y (2)

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 27 June 2022 Shift 2>Q 103

If the solution curve of the differential equation

((\tan^{- 1} y) - x) d y = (1 + y^{2}) d x

passes through the point

(1, 0)

then the abscissa of the point on the curve whose ordinate is

\tan (1)

is