EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 28 July 2022 Shift 2>Q 127

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IMPORTANT

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The differential equation of the family of circles passing through the points $(0, 2)$ and $(0, - 2)$ is

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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 - 29 July 2022 Shift 1>Q 128

Let the solution curve

y = y (x)

of the differential equation

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

pass through the point

(0, \frac{π}{2})

. Then,

\lim_{x \to \infty} e^{x} y (x)

is equal to

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 29 July 2022 Shift 2>Q 129

If the solution curve of the differential equation

\frac{d y}{d x} = \frac{x + y - 2}{x - y}

passes through the point

(2, 1)

and

(k + 1, 2), k > 0

, then

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 29 July 2022 Shift 2>Q 130

Let

y = y (x)

be the solution curve of the differential equation

\frac{d y}{d x} + (\frac{2 x^{2} + 11 x + 13}{x^{3} + 6 x^{2} + 11 x + 6}) y = \frac{(x + 3)}{x + 1}, x > - 1

, which passes through the point

(0, 1)

. Then

y (1)

is equal to

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 24 January 2023 Shift 1>Q 131

Let

y = y (x)

be the solution of the differential equation

x^{3} d y + (x y - 1) d x = 0, x > 0,

y (\frac{1}{2}) = 3 - e

. Then

y (1)

is equal to

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 24 January 2023 Shift 2>Q 132

Let

y = y (x)

be the solution of the differential equation

(x^{2} - 3 y^{2}) dx + 3 xy dy = 0, y (1) = 1

. Then

6 y^{2} (e)

is equal to

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 25 January 2023 Shift 1>Q 133

Let

y = y (x)

be the solution curve of the differential equation

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

,

x > 0, y (1) = 3

. Then

\frac{y^{2} (x)}{9}

is equal to :

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 25 January 2023 Shift 2>Q 134

Let

y = y (t)

be a solution of the differential equation

\frac{d y}{d t} + α y = γ e^{- β t}

Where,

α > 0, β > 0

and

γ > 0

. Then

{Lim}_{t \to \infty} y (t)

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 29 January 2023 Shift 1>Q 135

Let

y = f (x)

be the solution of the differential equation

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

. Then

\lim_{x \to 0^{+}} f (x)

is equal to