Mathematics Crash Course JEE Advanced>Chapter 25 - Differential Equations>Exercise 1>Q 11

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Suppose a curve whose sub-tangent is $n$ times the abscissa of the point of contact and passes through the point $(2, 3)$ . Then:

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Important Questions on Differential Equations

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Mathematics Crash Course JEE Advanced>Chapter 25 - Differential Equations>Exercise 1>Q 12

The function

f (x)

satisfying the equation,

f^{2} (x) + 4 f^{'} (x) \cdot f (x) + {[f^{'} (x)]}^{2} = 0

is -

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Mathematics Crash Course JEE Advanced>Chapter 25 - Differential Equations>Exercise 1>Q 13

A normal is drawn at a point

P (x, y)

of a curve. It meets the

x

-axis and the

y

-axis in point

A

and

B,

respectively, such that

\frac{1}{O A} + \frac{1}{O B} = 1,

where

O

is the origin, the equation of such a curve is a circle which passes through

(5, 4)

and has -

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Mathematics Crash Course JEE Advanced>Chapter 25 - Differential Equations>Exercise 1>Q 14

A function $y = f (x)$ satisfying the differential equation $\frac{d y}{d x} \sin x - y \cos x + \frac{\sin^{2} x}{x^{2}} = 0$ is such that, $y \to 0$ as $x \to \infty$ , then which of the following statements is/are correct?

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Mathematics Crash Course JEE Advanced>Chapter 25 - Differential Equations>Exercise 1>Q 15

Identify the statement(s) which is/are true?

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Mathematics Crash Course JEE Advanced>Chapter 25 - Differential Equations>Exercise 1>Q 16

Let

f : (0, \infty) \to R

be a differentiable function such that

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

for all

x \in (0, \infty)

and

f (1) \neq 1 .

Then

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Mathematics Crash Course JEE Advanced>Chapter 25 - Differential Equations>Exercise 1>Q 17

Let

f : [0, \infty) \to R

be a continuous function such that

f (x) = 1 - 2 x + \int_{0}^{x} e^{x - t} f (t) d t

for all

x \in [0, \infty) .

Then, which of the following statement(s) is (are) TRUE?

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Mathematics Crash Course JEE Advanced>Chapter 25 - Differential Equations>Exercise 1>Q 18

A differentiable function satisfies

f (x) = \int_{0}^{x} (f (t) \cos t - \cos (t - x)) d t

. Which of the following hold(s) good?

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Mathematics Crash Course JEE Advanced>Chapter 25 - Differential Equations>Exercise 1>Q 19

y = f (x)

has differential equation

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

, which is passing through the point

(0, 1) .

Then which of the following is/are true about the function?