Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 1>Q 8

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IMPORTANT

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The differential equation whose solution is $a x^{2} + b y^{2} = 1$ , where $a$ and $b$ are arbitrary constants, is of

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Important Questions on Differential Equations

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 1>Q 9

The differential equation of the family of circles having centre on

Y

-axis and radius

4

is

HARD

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 1>Q 10

The equation of the curve passing through the point

(- 1, - 2)

which satisfies

\frac{d y}{d x} = - x^{2} - \frac{1}{x^{3}}

is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 1>Q 11

The solution of the differential equation

\frac{d y}{d x} + \frac{1 + \cos 2 y}{1 - \cos 2 x} = 0

is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 1>Q 12

The solution of cos

(x + y) d y = d x

is

EASY

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 1>Q 13

Which of the following is true for $y (x)$ that satisfies the differential equation

$\frac{d y}{d x} = x y - 1 + x - y; y (0) = 0$

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 1>Q 14

If

y = y (x), y \in [0, \frac{π}{2})

is the solution of the differential equation

\sec y \frac{d y}{d x} - \sin (x + y) - \sin (x - y) = 0,

with

y (0) = 0

, then

5 y^{'} (\frac{π}{2})

is equal to _____.

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 1>Q 15

The solution of the differential equation

e^{\frac{d y}{d x}} = x + 1

when

y (0) = 3

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 9 - Differential Equations>Level 1>Q 16

The solution of the differential equation

\frac{d y}{d x} = e^{x - y} + x^{2} e^{- y}

will be