The pdf contains multiple type questions on the topic DIFFERENTIAL EQUATION.
The pdf contains the most important questions and covers all the topics in depth.
Answers have been also given on the last page.
CHAPTER-9
DIFFERENTIAL EQUATIONS
MULTIPLE CHOICE QUESTIONS
Q. NO. Questions
1. dy
Integration factor of differential equation + py = Q, where P and Q are functions of x is
dx
(a) ∫epdx
(b)
(c) e-∫pdx
(d) None of these
2. dy
The solution of = 1 + x + y + xy is
dx
(a) x – y = k(1 + xy)
2
x
(b) log (1 + y) = x + + k
2
2
y
(c) log (1 + x) + y + = k
2
(d) None of these
3. The degree of the differential equation
2
dy dy dy
( )² + ( )² = x sin
2
is
dx dx dx
(a) 1
(b) 2
(c) 3
(d) not defined
4. If y = e-x (A cos x + B sin x), then y is a solution of
2
dy dy
(a) +2 =02
dx dx
2
dy dy
(b) 2
–2 + 2y = 0
dx dx
2
dy dy
(c) + 2 + 2y = 0
2
dx dx
ZIET, BHUBANESWAR Page 1
, 2
dy
(d) 2
+ 2y = 0
dx
5. Solution of differential equation xdy – ydx = Q represents
(a) a rectangular hyperbola
(b) parabola whose vertex is at origin
(c) straight line passing through origin
(d) a circle whose centre is at origin
6. dy
Integrating factor of the differential equation cos x + y sin x = 1 is
dx
(a) cos x
(b) tan x
(c) sec x
(d) sin x
7. +1
dy y
The number of solutions of = when y(1) = 2 is
dx −1
x
(a) none
(b) one
(c) two
(d) infinite
8. dy
The differential equation y + x = c represents
dx
(a) Family of hyperbolas
(b) Family of parabolas
(c) Family of ellipses
(d) Family of circles
9. The curve for which the slope of the tangent at any point is equal to the ratio of the
abcissa to the ordinate of the point is
(a) an ellipse
(b) parabola
(c) circle
(d) rectangular hyperbola
10 dy
Thesolution of + y = e-x, y (0) = 0 is
. dx
(a) y = e-x (x – 1)
(b) y = xex
(c) y = xe-x + 1
(d) y = xe-x
11 The differential equation of the family of curves y² = 4a (x + a) is
. dy dy
(a) y² = 4 (x + )
dx dx
ZIET, BHUBANESWAR Page 2
, dy
(b) 2y = 4a
dx
2
d y dy
(c) y 2 + ( )² = 0
dx dx
dy dy
(d) 2x + y( )² – y
dx dx
2
12 dy dy
. Which of the following is the general solution of 2
–2 +y=0
dx dx
(a) y = (Ax + B)ex
(b) y = (Ax + B)e-x
(c) y = Aex + Be-x
(d) y = A cos x + B sin x
13 The differential equation of all straight lines passing through the origin is
. (a) y =
dy
(b) = y + x
dx
dy = y
(c)
dx x
(d) None of these
14 The differential equation for y = A cos αx + B sin αx where A and B are arbitary constants
. is
2
dy
(a) 2
– α²y = 0
dx
2
dy
(b) 2
+ α²y = 0
dx
2
dy
(c) 2
+ αy = 0
dx
2
dy
(d) 2
– αy = 0
dx
15 The degree of differential equation
2
. dy 3/2 d y
[1 + ( )²] = 2is
dx dx
(a) 4
(b) 3/2
(c) 2
(d) not defined
ZIET, BHUBANESWAR Page 3
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