9. The solution of

√^

(^) is:
(a)
(b) √
(c) √
(d) √
10. In order to solve the differential
equation x cos x^ + y (x sin x + cos x)=
1, the integrating factor is:
(a) x cos x (b) x sec x (c) x sin x (d) x
cosec x
11. The solution of the differential
equation

is:^
(a) y=^ ( )^ (b) y=
( )^ (c) y=^
( )^ (d) y=
(^ )
(^)
12. What are the order and degree
respectively, of the differential
equation representing the family of
curves ( (^) √ ), where c is a
positive parameter?
(a) 1, 2 (b) 1, 1 (c) 1, 3 (d) 1, 4
13. What does the solution of the
differential equation x dy – y dx= 0
represent?
(a) Rectangular hyperbola (b) Straight
line passing through (0, 0) (c) Parabola
with vertex at (0, 0) (d) Circle with
centre at (0, 0)
14. What is the degree of the equation
0
(^)
1 [^.
/

]

?

(a) 1 (b) 2 (c) 3 (d) 4

15. What are the order and degree

respectively of differential equation y =

x^?

(a) 1, 1 (b) 1, 2 (c) 2, 1 (d) 2, 2

16. What is the solution of y’= 1 + x +

, y (0)= 0?

(a) y=.^

/^ (b) y=^

(^) ( )
(c) y= ( ) (d) y= (
)
17. What is the equation of the curve
passing through the point. /
satisfying the differential equation sin x
cos y dx + cos x sin y dy= 0?
(a) cos x cos y= √ (b) sin x sin y= √
(c) sin x sin y=^ (d) cos x cos y=^
18. What is the degree of the
differential equation

.^

(^)
/
(^).
/^.
/^?^
(a) 3 (b) 2 (c)^ (d) Not defined
19. What is the solution of the
differential equation^ √^
?^
(a) (b)
(c) 2
(d) 2
where C is a constant.