Page 87 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

1 (c) 2 + x 2 = y c
factor . Then the relation between
x 2 x y
b and c is (d) 2 − 2 = c [JAM CA 2009]

=
=
(a) 2c b (b) b c 16. Consider the differential equation
dy 2 ( )
(c) 2b c+ = 0 (d) b + 2c = 0 dx − y = − y . Then lim y x is
x→ 
[JAM CA 2008] equal to

+
x
y
c
13. If e + xy + x sin y e = is the (a) -1 (b) 0
general solution of an exact (c) 1 (d) 
differential equation, then the
differential equation is [JAM CA 2010]

dy e − x y − sin y 17. An integrating factor of the
(a) = differential equation
−
dx e − y x x cos y
2
2xy dx + ( y − x 2 ) dy = is
0
dy e + x y + sin y
(b) = 1
+
dx e + y x x cos y (a) y (b)
y
x
y
dy − (e + + sin ) y 1 1
(c) = (c) (d)
+
dx e + y x x cos y y 2 y 3
x
y
dy − (e − − sin ) y [JAM CA 2010]
(d) =
−
dx e − y x x cos y 18. The general solution of the
differential equation
[JAM CA 2009] dy 2 )( − x 2 − 1 )
+
x
14. The general solution of dx = (1 y e − 2 tan y is
+
y 1 ( x + y 2 ) = y is (a) e x 2 tan y = 1 x c
−
+
(b) e − x 2 tan y = x c
=
=
2
(a) x cy + y (b) x cy − y 2
(c) e x tan y = x + 2 c
2
2
(c) y = cx + x (d) y = cx − x (d) e − x tan y = − 1 x + 3 c
[JAM CA 2011]
[JAM CA 2009]
)
g
0
19. If ( , x y dx + (x + ) y dy = is an
−
1
15. The general solution of y = 2 x y is exact differential equation and if
2
g ( ,0x ) = x , then the general
(a) 2 + − x 2 = − y c
solution of the differential equation is
(b) 2 − − x 2 = − y c
3
2
c
(a) 2x + 2xy + y =

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