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IMPORTANT

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If $y (t)$ is a solution of $(1 + t) \frac{d y}{d t} - t y = 1$ and $y (0) = - 1$ , then $y (1)$ is equal to

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Important Questions on Differential Equations

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Differential Equations>Competitive Thinking>Q 116

The solution of

d y = \cos x (2 - y cosec x) d x

, where

y = 2

when

x = \frac{π}{2}

, is

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Differential Equations>Competitive Thinking>Q 117

Let

y^{'} (x) + y (x) g^{'} (x) = g (x) g^{'} (x), y (0) = 0, x \in R

, where

f^{'} (x)

denotes

\frac{d}{d x} (f (x))

and

g (x)

is a given non-constant differentiable function on

R

with

g (0) = g (2) = 0

. Then the value of

y (2)

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Differential Equations>Competitive Thinking>Q 118

Let

y = y (x)

be the solution of the differential equation

\sin x \frac{d y}{d x} + y \cos x = 4 x, x \in (0, π)

. If

y (\frac{π}{2}) = 0

, then

y (\frac{π}{6})

is equal to

HARD

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Differential Equations>Competitive Thinking>Q 119

y (x)

satisfies the differential equation

y^{'} - y \tan x = 2 x \sec x

and

y (0) = 0

, then

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Differential Equations>Competitive Thinking>Q 120

The population of a city increases at the rate

3 %

per year. If at time

t

the population of city is

p

, then find the equation of

p

in time

t

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Differential Equations>Competitive Thinking>Q 121

Let

I

be the purchase value of an equipment and

V (t)

be the value after it has been used for

t

years. The value

V (t)

depreciates at a rate given by the differential equation

\frac{d V}{d t} = - k (T - t)

, where

k > 0

is a constant and

T

is the total life in years of the equipment. Then, the scrap value

V (T)

of the equipment is

MEDIUM

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Differential Equations>Competitive Thinking>Q 122

Let the population of rabbits surviving at a time

t

be governed by the differential equation

\frac{d p (t)}{d t} = \frac{1}{2} p (t) - 200

. If

p (0) = 100

, then

p (t)

equals

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 8 - Differential Equations>Evaluation Test>Q 1

The degree of the differential equation satisfying

\sqrt{1 - x^{4}} + \sqrt{1 - y^{4}} = a (x^{2} - y^{2})

If yt is a solution of 1+tdydt-ty=1 and y0=-1, then y1 is equal to

Important Questions on Differential Equations

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If $y (t)$ is a solution of $(1 + t) \frac{d y}{d t} - t y = 1$ and $y (0) = - 1$ , then $y (1)$ is equal to