f ( x ) is a continuous and differentiable function defined in x ∈ [ 0 , ∞ ) . If f ( 0 ) = 1 and f ' ( x ) > 3 f ( x ) ∀ x ≥ 0 , then

f ( x ) ≤ e - 3 x ∀ x ≥ 0

HARD

JEE Main/Advance

IMPORTANT

Earn 100

Solution of differential equation $x y (m y d x + n x d y) = \frac{x d y + y d x}{x^{m} y^{n}}$ , given $m + n = 1$ , is

50% studentsanswered this correctly

Important Questions on Differential Equations

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-2>Q 8

The equation of the curve which is such that the portion of the axis of

x

cut off between the origin and tangent at any point is proportional to the ordinate of that point is, where

a

is constant of proportionality and

b

is any constant (take base of logarithm as

e

)

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-2>Q 9

A curve passing through the point

(1, 1)

has the property that the perpendicular distance of the origin from the normal at any point

P

of the curve is equal to the distance of

P

from the

x

-axis. Then the equation of the curve is

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-2>Q 10

f (x)

is a continuous and differentiable function defined in

x \in [0, \infty) .

f (0) = 1

and

f^{'} (x) > 3 f (x) \forall x \geq 0

, then

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-2>Q 11

Solution of the equation

x \int_{0}^{x} y (t) d t = (x + 1) \int_{0}^{x} t y (t) d t, x > 0

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-2>Q 12

The solution of differential equation

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

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-2>Q 13

Find the curve which passes through the point

(2, 0)

such that the segment of the tangent between the point of tangency and the

y

–axis has a constant length equal to

2

units.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-2>Q 14

A

B

are two separate reservoirs of water. Capacity of reservoir

A

is double the capacity of reservoir

B

. Both the reservoirs are filled completely with water, their inlet are closed and then the water is released simultaneously from both the reservoirs. The rate of flow of water out of each reservoir at any instant of time is proportional to the quantity of water in the reservoir at that time. One hour after the water is released, the quantity of water in reservoir

A

1.5

times the quantity of water in reservoir

B

. After how many hours do both the reservoirs have the same quantity of water?

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 32 - Differential Equations>Exercise-2>Q 15

A tank contains

20 kg

of salt dissolved in

5000 L

of water. Brine that contains

0.03 kg

of salt per litre of water enters the tank at a rate of

25 L / \min

. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt remains in the tank after half an hour ?

Solution of differential equation xymydx+nxdy=xdy+ydxxmyn, given m+n=1, is

Important Questions on Differential Equations

Learn and Prepare for any exam you want !

Solution of differential equation $x y (m y d x + n x d y) = \frac{x d y + y d x}{x^{m} y^{n}}$ , given $m + n = 1$ , is