EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Differential Equations>JEE Advanced Paper 1 - 2016>Q 10

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JEE Advanced

IMPORTANT

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A solution curve of differential equation $(x^{2} + x y + 4 x + 2 y + 4) \frac{d y}{d x} - y^{2} = 0, x > 0$ passes through the point $(1, 3)$ . Then the solution curve -

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Important Questions on Differential Equations

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JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Differential Equations>JEE Advanced Paper 1 - 2016>Q 11

Let

f : (0, \infty) \to R

be a differentiable function such that

f^{'} (x) = 2 - \frac{f (x)}{x}

\forall x \in (0, \infty)

and

f (1) \neq 1

. Then,

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JEE Advanced

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Differential Equations>JEE Advanced Paper 1 - 2015>Q 12

Let

y (x)

be a solution of the differential equation

(1 + e^{x}) y^{'} + y e^{x} = 1 .

If

y (0) = 2

, then which of the following statements is (are) true?

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JEE Advanced

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Differential Equations>JEE Advanced Paper 1 - 2015>Q 13

Consider the family of all circles whose centers lie on the straight line

y = x .

If this family of circles is represented by the differential equation

P y^{"} + Q y^{'} + 1 = 0,

where

P, Q

are functions of

x, y & y^{'}

(y^{'} = \frac{d y}{d x}, y^{"} = \frac{d^{2} y}{d x^{2}})

, then which of the following statements is (are) true ?

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JEE Advanced

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Differential Equations>JEE Advanced Paper 1 - 2013>Q 14

Let $f : [\frac{1}{2}, 1] \to R$ (the set of all real numbers) be a positive, non-constant and differentiable function such that $f^{'} (x) < 2 f (x)$ and $f (\frac{1}{2}) = 1$ . Then the value of $\int_{1 / 2}^{1} f (x) d x$ lies in the interval:

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JEE Advanced

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Differential Equations>JEE Advanced Paper 1 - 2013>Q 15

A curve passes through the point

(1, \frac{π}{6})

. Let the slope of the curve at each point

(x, y)

be

\frac{y}{x} + \sec (\frac{y}{x}), x > 0

. Then the equation of the curve is