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Differential Equations MCQ Solutions

The document contains 20 multiple choice questions related to differential equations. The questions cover topics such as identifying the order and degree of differential equations, finding general and particular solutions, determining if equations are exact or linear, and identifying the type of curves represented by given differential equations.

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sanjay
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33 views3 pages

Differential Equations MCQ Solutions

The document contains 20 multiple choice questions related to differential equations. The questions cover topics such as identifying the order and degree of differential equations, finding general and particular solutions, determining if equations are exact or linear, and identifying the type of curves represented by given differential equations.

Uploaded by

sanjay
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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1.

2.

If (ey + 1) cos x dx + ey sin x dy = 0, then


(a) sin x (ey + 1) = C
(c) x sin (ey + 1) = C

dy
If cos2x dx + y = tan x, then
(a) y =(tan x -1) + Ce-tanx
(c) y = (tan x 1)+ Ce-cot x

3.

(b) cosx (ey + 1) = C


(d) x cos(ey + 1) = C

(b) y = (cot x 1) + Ce-tanx


(d) y = (cot x 1) + Ce-cotx

If (y + sinx cosx) dy + y (sinx + cosx) dx = 0.

y2
(a) y (-cosx + sinx) + 2 = C
y2
(c) y cos x sin x + 2 = C
4.

y2
(b) y(cosx sinx) + 2 = C
(d) None of these

If (x2y 2xy2)dx (x3-3x2y) dy = 0, then

x
y3
y
y2

1
n
C
2
x2
(a) y + 1n x = C (b) x
5.

x x
(b) log y + y = C

-x

(a) e (x + y ) = C (b) e (x -y ) = C

x
(d) log y -xy = C

(c) e (x y ) = C

(d) e

x2
2
-x y

=C

The order and degree of the differential equation

dy

dx
d2y
dx 2
(a) 2, 2
1, 6
8.

x
(c) log y + xy = C

(x2 + y2 + 2x) dx + 2ydy = 0 then

7.

(d) None

If (y xy2)dx-(x + x2y)dy = 0, then

x x
(a) log y - y = C
6.

x
y3
2
(c) y -1n x = C

3/ 2

= are respectively
(b) 2, 6

The degree of the differential equation

(c) 2, 3

(d)

d y

2
dx

y x

1
4

d3y
3
= dx is given by

(a) 2
9.

(b) 3

(c) 4

(d) 1

The order and degree of the differential equation

d y

dx 3

4
3

d2y
2
= dx is given by

(a) 1, 2
4, 8

(b) 2, 8

(c) 3, 8

10.

The general solution of the differential equation ydx- xdy = xydx is


(a) y = Axex
(b) Ax = yex
(c) y = Aex
(d) y = Ae-x

11.

The differential equation which is linear is

dy
x2 y
(a) dx
= sin y,
dy
(c) (1 + y) dx +sin x = 0
12.

13.

dy
(b) dx - x2y = sin x
dy
(d) dx + y (y + x) = x2

If (x + y) dx + (x y) dy = 0 then
(a) x2 + 2xy y2 = C
(c) x2 + 2xy + y2 = C

(b) x2 2xy y2 = C
(d) x2 2xy + y2 = C

An I.F. of the differential equation

dy
(1-x2) dx - xy = 1 is
(a) x

14.

15.

x
2
(b) 1 x

(c)

1 x

1
(d) 2 loge(1-x2)

dy
The solution of the differential equation dx = ex-y + x2e-y is
1
1
(a) ey = ex + 3 x2 + C
(b) ey = ex + 3 x3 + C
1
(c) ey = ex + x3 + C
(d) e-y = 3 x3 + ex +C
The differential equation ydx- 2xdy = 0 represents

(d)

(a) A family of straight lines


(c) A family of Cireles
16.

17.

(b) A family of Parabolas


(d) A family of Catenaries

Pdx + x siny dy = 0 is exact, then P can be


(a) siny + cos y
(b) sin y
(c) x2 cos y

The differential equation of the system of circles touching the y-axis at the origin
is

dy
(a) x2 + y2 2xy dx = 0,
dy
(c) x2 y2 + 2xy dx = 0,
18.

(d) cos y

dy
(b) x2 + y2 + 2xy dx = 0,
dy
(d) x2 y2 2xy dx = 0,

Differential equation of the parabolas having their axis parallel to the y-axis is

d 2 y dy
2
(a) dx + dx + y = 0

d2y
2
(b) dx + y2 = 0

d3y
3
(c) dx = 0

dy
(d) dx -

d3y
dx 3 =0

19.

20.

The orthogonal trajectory of the rectangular hyperbola dy = C 2 are given by


(a) y(x y) = k
(b) x2 y2 = k2
(c) x2 + y2 = k2
(d) x(x +
y) = k

1
2
The value of D a cos ax is
x
x
(a) 2a cos ax
(b) 2a sin ax
2

x
(c) 2a sin ax

(d) none of

these
Answers

1
A
11
B

2
A
12
A

3
A
13
C

4
A
14
A

5
D
15
B

6
A
16
C

7
A
17
C

8
C
18
C

9
C
19
B

10
B
20
B

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