Page 90 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations
=
)
−
(b) y = 2 ( 2 1 cos x (b) r a cos
)
+
0
(c) ( y y + ) 4 + cos x = (c) r = a (1 cos
)
+
)
−
(d) ( y y + ) 4 = ( 2 1 cos x (d) r = a (1 sin
36. The solution of the differential
[JAM GP 2010]
equation y + 11 4y = 0 subject to
33. The orthogonal trajectories of the y 1 y 1 2
curves y = 3x + + are ( ) 0 = , ( ) 0 = is
2
3
x c
(a) 2tan 3x + − 1 3ln y = k (a) sin2x + 1
(b) cos2x + 2x
(b) 3tan 3x + − 1 2ln y = k
(c) sin2x + cos2x
(c) 3tan 3x − − 1 2ln y = k
(d) sin2x − cos2x [JAM CA 2005]

(d) 3ln x − 2tan 3y = − 1 k 37. A particular solution of the

differential equation
[JAM CA 2006]
2
4
( D + 2D − ) 3 y e is
=
x
34. Orthogonal trajectories of the family
x
x
2
2
of curves (x − ) 1 + y + 2ax = are (a) (x + ) 1 e (b) xe
0
the solution of the differential xe x xe x
equation (c) 4 (d) 8
dy
2
+
2
(a) x − y − 1 2xy = 0 [JAM CA 2005]
dx 38. A particular solution of the
dy differential equation
2
2
1 2xy
(b) x + y − + = 0
1
11
y
dx y 111 − 3y + 3y − = e x cos2x is
dx 1 1
−
2
2
(c) x − y − 1 2xy = 0 (a) − e x sin2x (b) e x sin2x
dy 8 8
dx 1 x x
−
2
2
(d) x + y + 1 2xy = 0 (c) e cos2x (d) e sin2x
8
dy
[JAM CA 2005]
[JAM CA 2008]
35. The orthogonal trajectory of the 39. If ( ) 3y x = 1 1 y 1 ( ) 4x + y 2 ( ) x and
( )
)
cardioid r = a (1 cos , a being the y x = 1 2 ( ) 4y x + 1 ( ) 3y x , then
+
2
parameter, is y 1 ( ) x is
(a) r = a (1 cos− ) x 7x
(a) c e + c e
1 2

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