The solution of the differential equation d y d x = - x 2 + 3 y 2 3 x 2 + y 2 , y 1 = 0 is

log e x + y + 2 x y x + y 2 = 0

log e x + y - 2 x y x + y 2 = 0

The solution of the differential equation d y d x = - x 2 + 3 y 2 3 x 2 + y 2 , y 1 = 0 is

log e x + y + 2 x y x + y 2 = 0

log e x + y - 2 x y x + y 2 = 0

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

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IMPORTANT

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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 Questions on Differential Equations

MEDIUM

JEE Main

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

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JEE Main

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

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 29 January 2023 Shift 2>Q 136

Let

y = y (x)

be the solution of the differential equation

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

. If

y (2) = 2

, then

y (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 - 30 January 2023 Shift 1>Q 137

Let the solution curve $y = y (x)$ of the differential equation $\frac{d y}{d x} - \frac{3 x^{5} \tan^{- 1} (x^{3})}{{(1 + x^{6})}^{\frac{3}{2}}} y = 2 x$ $\exp \frac{x^{3} - \tan^{- 1} x^{3}}{\sqrt{(1 + x)^{6}}}$ pass through the origin. Then $y (1)$ is equal to: