EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 8th April 2018>Q 76

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JEE Main

IMPORTANT

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Let $y = y (x)$ be the solution of the differential equation $\sin x \frac{d y}{d x} + y \cos x = 4 x, x \in (0, π) .$ If $y (\frac{π}{2}) = 0,$ then $y (\frac{π}{6})$ 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 - 15th April 2018>Q 77

Let

y = y (x)

be the solution of the differential equation

\frac{d y}{d x} + 2 y = f (x)

, where

f (x) = \{\begin{matrix} 1, & x \in [0, 1] \\ 0, & o t h e r w i s e \end{matrix}

. If

y (0) = 0

, then

y (\frac{3}{2})

is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 16th April 2018>Q 78

The differential equation representing the family of ellipses having foci either on the

x

-axis or on the

y

-axis, center at the origin and passing through the point

(0, 3)

is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 2nd April 2017>Q 79

If

(2 + \sin x) \frac{d y}{d x} + (y + 1) \cos x = 0

and

y (0) = 1

, then

y (\frac{π}{2})

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 8th April 2017>Q 80

The curve satisfying the differential equation,

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

and passing through the point

(1, 1)

also passes through the point

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 9th April 2017>Q 81

A tangent to the curve,

y = f (x)

at

P (x, y)

meets

x

-axis at

A

and

y

-axis at

B

. If

A P : B P = 1 : 3

and

f (1) = 1,

then the curve also passes through the point

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 3rd April 2016>Q 82

If a curve

y = f (x)

passes through the point

(1, - 1)

and satisfies the differential equation,

y (1 + x y) d x = x d y,

then

f (- \frac{1}{2})

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 10th April 2016>Q 83

The solution of the differential equation

\frac{d y}{d x} + \frac{y}{2} \sec x = \frac{\tan x}{2 y}

, where

0 \leq x < \frac{π}{2}

and

y (0) = 1

, is given by

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 10th April 2015>Q 84

If

y (x)

is the solution of the differential equation

(x + 2) \frac{d y}{d x} = x^{2} + 4 x - 9, x \neq - 2

and

y (0) = 0,

then

y (- 4)

is equal to