EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Differential Equation>WBJEE 2018>Q 2

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IMPORTANT

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The differential equation representing the family of curves $y^{2} = 2 d (x + \sqrt{d}),$ where $d$ is a parameter, is of

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Important Questions on Differential Equation

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Differential Equation>WBJEE 2019>Q 3

General solution of

(x + y)^{2} \frac{d y}{d x} = a^{2}, a \neq 0

is

(C

is an arbitrary constant

)

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Differential Equation>WBJEE 2018>Q 4

The law of motion of a body moving along a straight line is

x = \frac{1}{2} v t

. x

being its distance from a fixed point on the line at time

t

and

v

is its velocity there. Then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Differential Equation>WBJEE 2020>Q 5

If

x \sin (\frac{y}{x}) d y = [y \sin (\frac{y}{x}) - x] d x, x > 0

and

y (1) = \frac{π}{2},

then the value of

\cos (\frac{y}{x})

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Differential Equation>WBJEE 2019>Q 6

The general solution of the differential equation

(1 + e^{\frac{x}{y}}) d x + (1 - \frac{x}{y}) e^{x / y} d y = 0

is

(C

is an arbitrary constant

)

HARD

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Differential Equation>WBJEE 2020>Q 7

Let

f

be a differentiable function with

\lim_{x \to \infty} f (x) = 0 .

If

y^{'} + y f^{'} (x) - f (x) f^{'} (x) = 0

,

\lim_{x \to \infty} y (x) = 0,

then (where

y^{'} \equiv \frac{d y}{d x})

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Differential Equation>WBJEE 2018>Q 8

Let

y (x)

be a solution of

(1 + x^{2}) \frac{d y}{d x} + 2 x y - 4 x^{2} = 0

and

y (0) = - 1 .

Then

y (1)

is equal to