Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 10 - Differential Equations>DPP>Q 9

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JEE Main

IMPORTANT

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The family of curves passing through $(0, 0)$ and satisfying the differential equation $\frac{y_{2}}{y_{1}} = 1$ (where $y_{n} = \frac{d^{n} y}{d x^{n}}$ ), is

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Important Questions on Differential Equations

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 10 - Differential Equations>DPP>Q 10

The solution of the differential equation

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

is:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 10 - Differential Equations>DPP>Q 11

The solution of differential equation

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

is

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 10 - Differential Equations>DPP>Q 12

The differential equation for the family of curves

y = c \sin x

can be given by

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 10 - Differential Equations>DPP>Q 13

If the solution of the equation

\frac{d^{2} x}{d t^{2}} + 4 \frac{d x}{d t} + 3 x = 0

given that for

t = 0, x = 0

and

\frac{d x}{d t} = 12

is in the form

x = A e^{- 3 t} + B e^{- t}

, then

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 10 - Differential Equations>DPP>Q 14

The solution of

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

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 10 - Differential Equations>DPP>Q 15

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

has the solution

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 10 - Differential Equations>DPP>Q 1

If

y (t)

satisfies the differential equation

y^{'} (t) + 2 y (t) = 2 e^{- 2 t}, y (0) = 2

, then

y (1)

equals

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 10 - Differential Equations>DPP>Q 2

If

\frac{d y}{d x} - y \log_{e} 2 = 2^{s i n x} (\cos x - 1) \log_{e} 2

, then

y =

?