MULTIPLE CHOICE QUESTIONS
CHAPTER – 9 DIFFERENTIAL EQUATIONS
3
 d 2 y   dy 
 dy 
Q1. The degree of the differential equation  2      sin    1  0 is:
 dx 
 dx   dx 
(a) 3
2
(b) 2
(c) 1
(d) not defined
d2y
dy
Q2. The order of the differential equation 2 x
 3  y  0 is:
2
dx
dx
2
(a) 2
(b) 1
(c) 0

(d) not defined

Q3. The solution of the differential equation e x 1 y dy   y 1 e x dx is:


(a) e y  c e x 1  y 1

Q4. The solution of the differential equation
(a) e1 y  x 
x2
c
2


(d) none of these
dy
1  x  y  xy is:
dx
(b) log 1  y  x 
Q5. The solution of the differential equation

(c) y  e x 1  y 1
(b) e y  c e x  y 1
x2
c
2
(c) e y  x 
x2
c
2
(d) none of these
dy
1 y 2

 0 is:
dx
1 x2
(a) y  sin 1 y  sin 1 x  c (b) sin 1 y  sin 1 x  c
(c) sin 1 y  sin 1 x  c
(d) none of these
Q6. The solution of the differential equation x 1 y 2 dx  y 1 x 2 dy  0 is:
(a) sin 1 x  sin 1 y  c
Q7. The solution of the differential equation
(a) x 2  y 2  cx
(d) none of these
dy y 2  x 2
is:

dx
2 xy
(b) x 2  y 2  cy
Q8. The solution of the differential equation
(a) y  sin x  c cos x
(c) tan 1 x  tan 1 y  c
(b) 1 x 2  1 y 2  c
(c) x 2  y 2  cx
(d) none of these
dy
 y tan x  sec x is:
dx
(b) y  sin x  c cos x
(c)  y  sin x  sin x  c
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(d) none of these
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Q9. The integrating factor of the differential equation  x log x 
(a) log  log x 
(b) e x
dy
 y  2log x is:
dx
(c) log x
Q10. The solution of the differential equation
(d) x
dy y
  sin x is:
dx x
(a) x  y  cos x   sin x  c (b) x  y  cos x   sin x  c (c) x  y  cos x   cos x  c
Q11. The solution of the differential equation 2 x
(a) circles
(a) sin
dy
 y  3 represents:
dx
(b) straight lines
(c) ellipses
Q12. The solution of the differential equation x
x
 xc
y
(b) sin
(d) parabolas
dy
y
 y  x tan is:
dx
x
y
 cx
x
(c) sin
Q13. The solution of the differential equation x 2  y 2
(a) x2  y 2 12 x  c
(d) none of these
(b) x2  y 2  3x  c
x
 cy
y
(d) sin
y
 cy
x
dy
 4 is:
dx
(d) x3  y3 12 x  c
`(c) x3  y3  3x  c
Q14. The solution of the differential equation x dx  y dy  x 2 y dy  y 2 x dx is:

(a) x 2 1 c 1 y 2


(b) x 2 1  c 1 y 2



(c) x3 1 c 1 y 3
 y
 dy
dx
Q15. The solution of the differential equation x 2  1
(a) y  2  x 2
(b) y 
1 x
1 x

(d) x3 1  c 1 y 3

 1  0 is:
(c) y  x  x 1
Q16. The solution of the differential equation
x
(a) tan 1    log y  c
 y
2

(d) y 
1 x
1 x
dy x 2  xy  y 2

is:
dx
x2
x
 y
(b) tan 1    log x  c (c) tan 1    log x  c
x
 y
(d) none of these
ANSWERS
1. d
d
2. a
3. a
16. d
4. b
5. c
6. b
7. c
8. b
9. c
10. a
11. d
12. b
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13. d
14. a 15.
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