Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Work Book Exercise 12.4>Q 6

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JEE Advanced

IMPORTANT

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If $\cos^{2} x \frac{d y}{d x} - y \tan 2 x = \cos^{4} x,$ where $| x | < \frac{π}{4}$ and $y (\frac{π}{6}) = \frac{3 \sqrt{3}}{8}$ , then the constant term in the solution of the differential equation is

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Important Questions on Differential Equations

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Work Book Exercise 12.4>Q 7

The solution of the equation

x^{2} y - x^{3} \frac{d y}{d x} = y^{4} \cos x,

when

y (0) = 1

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Work Book Exercise 12.4>Q 8

The solution of the differential equation

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

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Work Book Exercise 12.4>Q 9

The solution of

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

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Work Book Exercise 12.5>Q 1

The equation of the curve whose tangent at any point

(x, y)

makes an angle

\tan^{- 1} (2 x + 3 y)

with

X

-axis and which passes through

(1, 2),

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Work Book Exercise 12.5>Q 2

A curve having the condition that the slope of tangent at some point is two times the slope of the straight line joining the same point to the origin of coordinates, is a/an

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Work Book Exercise 12.5>Q 3

The equation of the curve satisfying the differential equation

y_{2} (x^{2} + 1) = 2 x y_{1}

passing through the point

(0, 1)

and having slope of tangent at

x = 0

as

3

, is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Work Book Exercise 12.5>Q 4

The equation of the curve whose sub-normal is equal to a constant

a

, is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Work Book Exercise 12.5>Q 5

The slope at any point of a curve

y = f (x)

is given by

\frac{d y}{d x} = 3 x^{2}

and it passes through

(- 1, 1)

The equation of the curve is